02 Nov 2020

Bob Murphy Twin Spin

Bob Murphy Show 46 Comments

==> Here’s my article on Arrow’s Impossibility Theorem, in time for Election Day…

==> In ep. 159 of the Bob Murphy Show, I discuss left vs. right and libertarianism with Greg Gordon. Audio here, video below:

46 Responses to “Bob Murphy Twin Spin”

  1. Harold says:

    I like the Arrow article. Instead of focusing on the No Dictator clause, which is difficult, focusing on transitivity is much easier. This gets the idea across without mental gymnastics.

    Essentially, since all such voting systems will result in “bad” outcomes in some instances (if by bad we mean transgresses one of Arrow’s axioms), the solution would seem to be which is likely to produce the least bad outcome. It seems likely that a first past the post will fail to represent society very well if there are more than 2 possibilities, but a transferable vote or instant run off system seems more likely to do so. I have seen that this is used in some of the current USA elections.

    It would not help in the example you give, since everybody has the same number of first choices so it is not possible to remove any candidate. In practice, this is unlikely to occur in a vote of larger size. It does not solve all the problems but does at least allow 3rd party candidates a chance.

    Exploring a bit, if we had the 3 voters T/J/B either 1/2/3 or 3/2/1, with nearly everyone preferring either T or B. The alternative vote would reject J in the first round and there would be no votes to re-distribute. J would still need to get over 1/3 of the number one choices to progress. But voters would be able to vote J number 1, knowing that if this fails, their vote would not go to their least favoured candidate. Both T and B voters could opt to vote for J and still be sure their vote will not help their hated candidate. This is not new, and just some musings really. There was a referendum fairly recently in the UK on AV. The pro first-past-the post campaign could point out the problems with AV, which seem strange and undesirable. The AV campaign got no traction with pointing out the problems with FPTP because we are used to them and they seem normal to us and not so undesirable.

    How does the AV system work out in States that use it in the US?

    Quadratic voting is another possibility, the deficits of which are much less that they first appear. However, QV is not likely to become popular because it violates some widely accepted norms.

    Another system would cardinal voting, which allow individuals voters to distribute say 100 votes across all candidates to express their degree of liking as well as ranking their preference. In the above example, if everybody gave 60 to their preferred candidate, none to their hated candidate and 40 to J, then J would win handsomely. This avoids Arrrow’s Impossibility Theorem, which requires ordinal preferences, and thus would avoids your conclusion that the whole project is built on quicksand.

    An interesting with Arrow on this subject.

    He does say that no system can guarantee not transgressing one of his axioms, it is possible that any system in practice will obey them all.

  2. Harold says:

    Interesting position concerning run off elections. In Georgia, Purdue is at 49.997%, with 50% required to avoid a run off. I don’t know if anything will change, but the tiniest of margins. Pretty much all of the second place votes would have to go against him to change the result.

    • Harold says:

      I have realized that the run off is an actual new election, not a redistribution. What fun! Just what we need, another election.

      • Tel says:

        That’s generally normal for a run-off, given that voters don’t put down their full list of preferences.

        The concept of a run off as a whole new election is actually not even supported as a possibility when looking at Arrow’s Theorem … despite many jurisdictions making that their standard approach. There’s a whole larger class of election styles (e.g. having party primaries) where voters progressively reveal more information, while getting feedback from earlier rounds to learn what other voters are doing. Arrow ignores all of those.

        You still get strategic voting, and the occasional questionable situation where the first round is close to a three-way tie … sufficiently close that there might be questions as to who should be in the run off. I think that is a rare situation, and not worth worrying about. Just accept that strategic approaches are normal for many parts of life … even doing a business deal you find that most people don’t reveal their actual price limit, they are hoping to get it at a slightly better price if they can.

        • Harold says:

          Yes, I had just been reading about instant run offs in the USA and just presumed this was one of them.

          I don’t think many elections are intended to produce an unambiguous ranking of societies preferences, which is what Arrow showed cannot always happen with any system. The run off is designed to produce the one with a majority of all votes not just a plurality. Some of his criteria are more or less presumed to apply, such as preference for A over B is not affected by candiadate C. In an instant run off this is presumed, but with an actual run off this does not have to be the case. You are allowed to prefer A over B if C is running, but when C drops out you can prefer B over A. I susect this is unusual. People may change their minds between elctions, but I would think not because the other candidates are no longer running.

  3. Transformer says:

    I think I finally understood the ‘No Dictator clause’!

    if you have the task of designing a set of rules for ranking preferences within a community that are consistent with the following 2 clauses:

    – if every citizen thinks outcome A is preferable to outcome B, then it better be the case that the procedure spits out the result that “society” prefers A to B.

    – the “social” ranking of outcome A versus B should only depend on how the citizens compare A to B

    Then the only rule that could do this is one that gives a specific individual in the community the right to specify all the societal rankings. This rule would break the ‘No Dictator clause’ and hence the given task is impossible.

    Is that correct ?

    • Transformer says:

      Should have said ‘In effect gives a specific individual in the community the ability to specify all the societal rankings’ since in reality the rules may be more sophisticated but still lead to the ‘dictator’ conclusion.

      • Harold says:

        I think your clarification is important. Nobody is given the “right” to decide, it is just that it works out that the popular choice always lines up with one person’s vote, making them a dictator. I think.

      • Harold says:

        It is also important to note that whilst the dictator cannot be ruled out, it is very unlikely to happen in practice.

        • Transformer says:

          Thanks Harold.

          For me this was an intellectual exercise to fully understanding the theorem. Oddly, I’d previously been able to follow the proofs but never quite got my head around what kind of rules for social ordering would be possible if one ignored the ‘dictatorship clause’ but applied the others and thinking about it again after Bob’s post I concluded that they really would boil down to ‘Person X gets to choose all the rankings’ as all other sets of rules would violate the other requirements in some situations.

          BTW: I agree that by relaxing in various ways the other 2 requirements but keeping the dictatorship clause one can come up with workable rules for social rankings – Arrow is simply telling us that all of them will be flawed in some ways in some situations.

          • Transformer says:

            Here is an example of how I see the rules might work in Bob’s scenario to create a dictator:

            In the preferences that Bob gives he shows that there is no obvious way to rank the candidates based purely on the stated preferences.

            Suppose they have a rule that says that when this happens then the oldest voter gets to choose the winner and Alice is the oldest voter.

            Application of Arrow’s theorem then shows that as Alice is the only person to prefer Biden above Trump this will make her the dictator over all rankings in all future elections as well !

            More generally: Whenever the rules used to determine the rankings for a particular vote leads to a result where an individual is the only person to select a ranking for a specific pairing then that individual can be shown by the theorem to become the dictator over all pairings for all future votes as well.

            (BTW: This is probably really really obvious to everyone else – I’ve just been struggling to get my head around it and think I’m finally getting there!)

            • Bob Murphy says:

              Transformer, if you email me I can send you the actual proof of Arrow’s theorem (based on Sen’s amazing version).

              Also, soon I will do a podcast episode on this stuff, that might clarify.

            • random person says:

              Transformer wrote,

              More generally: Whenever the rules used to determine the rankings for a particular vote leads to a result where an individual is the only person to select a ranking for a specific pairing then that individual can be shown by the theorem to become the dictator over all pairings for all future votes as well.

              Except that since humans cannot be persuaded to consistently stick to any particular rule of decision making, history has never produced such a dictator. That’s not to say that there haven’t been many dictators/kings/monarchs/emperors/whatever we choose to call them, but none of them have ever possessed the absolute power to structure society according to their wishes. One demonstration of this is how many of them were removed from power by means of murder.

              Harold and I were talking about this at length down here.

            • Harold says:

              Landsburg did a post on this a while ago.
              He expressed approximately it thus.

              if you have two people (Alice and Bob) with three choices (A,B,C), they vote and if Alice and Bob agree the choice is simple. It is only if they disagree there is a problem. They may decide to give Alice preference in the one instance that she prefers A and Bob prefers B.

              That alone does not at first sight appear to make her a dictator because it does not mean that Alice should prevail in the case of Alice preferring B and Bob preferring C or Alice preferring B and Bob A.

              What Arrow’s theorem shows is that if you hold to the other axioms and you give Alice preference in the case of A vs B, then Alice must prevail in all situations and becomes the dictator.

              What could happen is that one of the other axioms is broken, and Alice is no longer a dictator. They could decide that if they disagree they get the option that was not preferred by either. Or that on some days Bob gets his way. These would break one of the other axioms. Such as “It must deterministically provide the same ranking each time voters’ preferences are presented the same way.” Void that one and we avoid the dictator, which I suggest is what would happen in the Alice and Bob case.

              • random person says:

                These would break one of the other axioms. Such as “It must deterministically provide the same ranking each time voters’ preferences are presented the same way.” Void that one and we avoid the dictator, which I suggest is what would happen in the Alice and Bob case.

                Yes, I think that is the point I am making. Real life will not deterministically provide the same outcome each time the voters’ preferences are presented in the same way (if they ever are presented the same way to begin with). There will always be an element of chaos caused by people being people. It is not even reasonable to expect this axiom to ever be followed in real life.

                Also, Alice and Bob might very well look at options A, B, and C, and ask, “Who is giving us only these three options?” and agree that they both want option D, which was not included in the three options they were given.

                For example, a highway robber might stop Alice and Bob on a road and tell them he is holding an election where they have the following three options:
                a) To give him all their money and valuables (that they have with them), and be allowed to walk away
                b) to come with him and be subjected to forced labor for a year, but get their stuff back after that time
                c) to die, leaving him all their money and valuables (that they have with them)

                I am not sure why a highway robber would do this, but bear with me.

                Alice and Bob might look at the highway robber, decide they can take him, and go with option D, attempt to club the highway robber on the head and take his money and valuables instead. The outcome would presumably depend on who won the ensuing fight.

                An interesting real life example of people turning out en masse to vote “none of the above” is Peru’s recent elections. It will be interesting to see how this plays out over the years.

                From the Washington Post article, “Lessons from Peru’s revolt against all political parties” by Francisco Toro and
                James Bosworth

                It sounds like a joke, but Peruvians woke up to it splashed across their headlines this week. In a country where voting is compulsory by law, people dissatisfied with their options risk a fine if they stay home. So instead they turned out this Sunday … and cast more than twice as many spoiled and blank ballots as they did ballots for the most popular party.

                While Peruvians were certain they didn’t like the parties in their last Congress, the country did not coalesce around an alternative. The result is that as many as 10 parties will have seats in Congress even though no party received more than 10 percent of the total vote once blank and null ballots are included. More than a quarter of voters split their votes across a dozen parties so small that they received fewer than the 5 percent of votes necessary to get a seat in the next Congress. According to Monday morning vote tallies, 22.5 percent had cast spoiled or blank ballots.

                Long story short, “none of the above” won by a landslide.


              • Transformer says:

                The Wikipedia article https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem
                has quite a nice ‘informal proof’ where the voting is set up in a specific way such that the rankings are a->b->c and if everything is held constant except that a single voter changes his vote to move B above A then not only does this switch societal preference to put B above A, but (crucially) means that as long as this voter ranks B above C then this is the societal ranking even if no-one else votes for B above C.

                This makes him B/C dictator and therefore (the informal proof goes on to demonstrate) dictator over all pairings.

              • Transformer says:

                @Bob, Thanks ! (I think I have the notes with your proof from last time this came up on the blog,)

              • Harold says:

                Transformer – I saw that one also and thought it was good.

                Random – we could think of the election with the highwayman as having 4 choices, A,B,C and D. If they agree, there is no problem, as above. Only when they disagree is there an issue. If Alice wants to fight she cannot without the agreement of Bob. Arrow still applies.

                The Wikipedia article demonstrates that this applies when there are more than 2 people, up to any number.

    • random person says:

      From Murphy’s article,

      Nondictatorship: there shouldn’t exist one person in society such that, no matter what everyone else says, the procedure always makes the “social” ranking identical to the one person’s preferences.

      Terry Pratchett’s rule on the death of kings: Murder is natural causes for a king, makes it nearly impossible for a literally absolute dictator to exist. (That’s not to say that there’s no such thing as an “absolute dictator”, but that “absolute” shouldn’t be taken literally, but rather to mean “extremely oppressive”.)

      Any king/dictator/emperor/monarch/Augustus/Caesar (or whatever we want to call dictators) will almost certainly get murdered eventually if he angers enough people (or, perhaps more to the point, specific people), and in particular, if he angers those with frequent access to his physical person. The only exception I could conceivably think of, is if the dictator commands the loyalty of so many powerful robots and AI, that human cooperation is no longer relevant to him staying in power, which could be an issue in the future, but hasn’t been historically.

      This doesn’t mean he can’t still be extremely oppressive, up to and including perpetrating widescale genocide and forced labor. It simply means that, in order to avoid being murdered and therefore stay in power, he at least needs to keep the loyalty of enough people with weapons, particularly those with access to his physical person.

      Roman history provides numerous examples of Terry Pratchett’s rule. I include some who died in battle or of battle wounds, even if for whatever reason dying in battle isn’t always classified as “murder” by many historians. Historical accounts being unclear or inconsistent at times, and I have included some who may or may not have been killed. I have also included Eastern Roman emperors who were murdered, possibly murdered, or died in battle.

      * Romulus may or may not have been murdered in 716 BC.
      * Tullus Hostilius may or may not have been assassinated by Ancus Marcius in 642 BC.
      * Lucius Tarquinius Priscus was assassinated in 579 BC.
      * Servius Tullius was murdered by Tarquinius and his men in 535 BC.
      * Julius Caesar was stabbed to death in 44 BC.
      * Gaius Caligula was murdered by Praetorian guard officers, lead by Cassius Chaerea, in 41 AD. Allegedly, many in the senate, army and equestrian order were also aware of and involved in the conspiracy.
      * Claudius was most likely poisoned to death in 54 AD, probably by his wife, Agrippina.
      * Galba was murdered in a mutiny lead by Otho in 69 AD.
      * Vitellius was murdered by troops of Vespasian in 69 AD.
      * Domitian was stabbed to death by a steward in 96 AD, in a conspiracy involving court officials. The steward had feigned an arm injury so that he could conceal a dagger in the bandage, and also died as a result of a wound from his struggle with Domitian.
      * Commodus was strangled to death by his wrestling partner, Narcissus, in 192 AD, after a failed poisoning attempt by a conspiracy involving several people.
      * Pertinax was assassinated by a member of the Praetorian Guard in 193 AD.
      * Didius Julianus was killed by a soldier in the palace in 193 AD, after being sentenced to death by the Senate.
      * Geta was murdered by centurions on the orders of his brother, Caracalla, in 211 AD.
      * Caracalla was stabbed to death by a soldier, Justin Martialis, in 217 AD.
      * Macrinus was executed in 218 AD.
      * Diadumenianm, Macrinus’s son and co-emperor, was executed in AD 218.
      * Elagabulus was murdered by the Praetorian Guard in 222 AD.
      * Severus Alexander was murdered in a legionary mutiny in 235 AD.
      * Maximinius Thrax was murdered by soldiers in 238 AD.
      * Pupienus Maximus was murdered by the Praetorian Guard in 238 AD.
      * Balbinus, Pupienus’s co-emperor, was murdered by the Praetorian Guard in 238 AD. The Praetorian Guard apparently resented serving under senate-appointed emperors.
      * Phillip the Arab was either killed it battle or murdered by his soldiers while being overthrown by Decius in 249 AD.
      * Philip II, Phillip the Arab’s son and co-emperor, was either killed with Phillip the Arab in battle, or assassinated by the Praetorian Guard after news of Philip the Arab’s death reached Rome.
      * Decius died in battle against the Goths in 251 AD.
      * Herennius Etruscus, Decius’s son and co-emperor, also died in battle against the Goths in 251 AD.
      * It is unclear whether Hostilian died by plague or by murder in 251 AD.
      * Gallus was killed in 253 AD, likely by his own troops.
      * Volusianus, Gallus’s son and co-emperor, was also killed in 253 AD, likely by their own troops.
      * Aemilianus was murdered in a legionary mutiny in 253 AD.
      * Valerian was taken captive by the Persians, and allegedly murdered by them after some period of captivity.
      * Saloninus, son and co-emperor of Gallienus, was killed in 260 AD by troops of Postumus.
      * Gallienus was murdered during the battle of Naissus in 268 AD.
      * Sources differ on why Quintillus died in 270 AD, but some allege murder.
      * Aurelian was murdered by the Praetorian Guard in 272 AD, after a secretary, fearful of Aurelian’s harsh punishments, forged a document listing various names of high officials as marked for execution and used the forged document to start a conspiracy to kill Aurelian.
      * Tacitus died in 276 AD, though accounts differ on whether he died of fever or was assassinated.
      * Florianus was killed by his own soldiers in 276 AD.
      * Probus was murdered by his own soldiers in 282 AD.
      * Carinus was killed in 285 AD, possibly by a tribune.
      * Valerius Severus was killed or forced to commit suicide in 307 AD.
      * Licinius was executed on the orders of Constantine I in 325 AD, after having been defeated in battle in 324 AD.
      * Constantine II was killed in an ambush outside Aquileia in 340 AD.
      * Constans I was murdered by supporters of Magnetius in 350 AD.
      * Julian died of a battle wound in 363 AD.
      * Valen died at a battle in 378 AD.
      * Gratian was murdered by Andragathius, who was sent by Maximus, in 383 AD, after his troops deserted him.
      * Valentinian II was probably murdered by Arbogast, or Praetorians paid by Arbogast, in 392 AD, although Arbogast claimed Valentinian II had committed suicide.
      * Eugenius was executed in 394 AD, after losing a battle against Theodosius I.
      * Joannes was decapitated in 425 AD.
      * Valentinan III was assassinated by followers of Flavius Aetius in 455 AD.
      * Petronius Maximus was killed in 455 AD, either by rioters or a Roman soldier.
      * Accounts of Avitus’s death in 456 or 457 AD vary, but some allege murder.
      * Anthemius was executed by Gundobad or Ricimir in 472 AD.
      * Basiliscus was enclosed in a dry cistern, to die of exposure, in 476 AD, on the orders of Zeno.
      * Julius Nepos was murdered, likely by his own soldiers, in 480 AD.
      * Maurice I AD was murdered during a mutiny in 602 AD.
      * Theodosius, son and co-emperor of Maurice, was executed in 602 AD.
      * Phocas “the Tyrant” was beheaded by Heraclius in 610 AD.
      * Constans II was assassinated by his chamberlain in 668 AD, while he was bathing.
      * Leontis was beheaded on the orders of Justinian II in 705 AD or 706 AD.
      * Tiberius III was beheaded on the orders if Justinian II in 705 AD or 706 AD.
      * Justinian II “Rhinotmetus” was executed during a rebellion in 711 AD.
      * Anastasios II was put to death on the orders of Leo III in 719 AD.
      * Constantine VI was captured, blinded, and imprisoned in 797 AD, and it’s possible he may have died of his wounds shortly after.
      * Nikephoros I was decapitated in 811 AD, on the orders of Krum, Khan of Bulgaria.
      * Staurakios died of either gangrene or poisoning in 812 AD.
      * Leo V “the Armenian” was assassinated by supporters of Michael the Amorian in 820 AD.
      * Michael III was assassinated by John of Chaldia, in a conspiracy organized by Basil the Macedonian, in 867 AD.
      * Constantine VII died in 959 AD, and may or may not have been poisoned.
      * Nicephoros II Phocas was assassinated by John Tzimisces, his wife’s lover, in 969 AD.
      * John I Tzimiskes died in 976 AD, and may or may not have been poisoned by Imperial Chamberlain Basil Lekapenos.
      * Romanus III died in 1034 AD, possibly poisoned by his wife.
      * Romanos IV Diogenes died of wounds in 1072 AD, as a result of having been deliberately blinded by men sent by John Doukas.
      * Konstantios Doukas died in battle in 1081 AD.
      * Alexius II Comnenus was murdered in 1183 AD, on the orders of Andronicus Comnenos.

      • Harold says:

        Nero possibly killed himself in AD 68 after being sentenced to death. i think that qualifies as a dictator annoying enough people to result in their death.

        It was a tough proposition, dying of old age as a Roman emperor.

        Diocletian managed it. He was the first to abdicate and lived out his life in his palace tending his vegetables.

        Generally successful, he set up the empire for the next century or so.

        He had (at least) 2 notable failures pertinent to this blog. He failed to control inflation by price controls. And he failed to eradicate Christianity in the last official persecution. His protege Constantine established Christianity as the official religion.

        However, in the context of this post, the dictator in the dictator clause is not really this type of dictator. I wonder if Arrow could have used a different term.

        • random person says:

          Harold wrote,

          However, in the context of this post, the dictator in the dictator clause is not really this type of dictator. I wonder if Arrow could have used a different term.

          I brought it up because theoreticians of human behavior often forget that human behavior tends not to fit neatly into mathematical theorems.

          I can’t think of any dictator in actual human history, even the ones we call “absolute dictators”, who actually held the sort of power Arrow (or Arrow as interpreted by Murphy) describes.

          What Arrow (or Arrow as interpreted by Murphy) is describing sounds more like an omnipotent God, but without the morals often ascribed to God by various theologies.

          Incidentally, democracy doesn’t work the way Arrow (or Arrow as interpreted by Murphy) describes either, not just for the reasons Arrow says it doesn’t work, but because there’s just no way to make human beings consistently follow any particular rule of decision-making consistently. Even if Arrow had found a particular set of procedures that met his criteria, there would be no way to make people consistently follow them. Actual human beings are inherently chaotic.

          Nor are his criteria necessarily the most helpful. More relevant criteria might be “Can we all at least agree not to commit genocide and other atrocities against each other? No? Well, is there at least anything we can do to mitigate the risks of committing genocide and other atrocities against each other?”

          There is a debate about whether democracy prevents genocide, and if so, to what extent. Rudolph Rummel argued that democracy offers significant, although not absolute, protection against genocide. On the other side, Michael Mann argues that democracy has a dark side that encourages genocide. Even if we assume that democracy has some preventative effect against genocide, there are certainly plenty of caveats.

          Democracy doesn’t seem to protect people who can’t vote in the democracy – e.g. democracy in the United States doesn’t protect Guatemalans from US-backed genocide, because Guatemalans can’t vote in US elections. Being able to vote also won’t necessarily protect minorities who can easily be outvoted. Since there are no pure democracies, there also exists risks from non-democratic institutions within societies generally considered democratic, such as the American CIA, which was involved in the Guatemalan genocide. Democratic institutions also can’t always protect democratically elected leaders from being assassinated and replaced by dictators. For example, after decades of forced labor and other atrocities under the rule of King Leopold II and then of Belgium, the Congolese were suddenly allowed to vote (without forced labor having been fully abolished first), and, predictably, elected an anti-forced labor Prime Minister, Lumumba. Lumumba was, after less than a year in office, removed from power by the CIA, and assassinated in a Belgian plot (both the CIA and the Belgians receiving assistance from Congolese collaborators) to eventually be replaced by Mobutu, a dictator, who ruled with considerable backing from the CIA and committed many atrocities.

          • Harold says:

            Arrow’s dictator only has any sort of power in an election, so avoiding elections avoids this issue entirely.

            The dictator axiom can be avoided if one of the other axioms are broken.

            If the other axioms are held to, then it is impossible for the “social welfare function” (i think) not to represent the will of one voter.

            • random person says:

              Arguably, every decision a person makes is a sort of election. Perhaps I elect to eat Greek yogurt for breakfast in the morning. Perhaps someone else elects to eat pancakes for breakfast, another elects to eat oatmeal for breakfast, and yet another elects to skip breakfast that day.

              A dictator might elect to debase the currency; a street vendor might then elect to raise his prices, and so on and so forth. The laws of physics have so far prevented anyone on Earth from getting enough power to totally prevent other people from having their own elections. (Torture comes close to preventing an individual from holding their own elections, but doesn’t completely negate free will, as people who have resisted torture demonstrate, though it may come close. However, even the most brutal dictators haven’t managed to personally torture everyone in any sizable society. The torturers themselves can elect to follow the dictator’s instructions and torture people, or to not follow the dictator’s instructions and refuse to torture people.)

        • random person says:

          Harold wrote,

          Nero possibly killed himself in AD 68 after being sentenced to death. i think that qualifies as a dictator annoying enough people to result in their death.

          That’s a fair point. I omitted a number of suicides because they didn’t technically meet the criteria of the king/dictator/emperor/monarch/Augustus/Caesar/whatever dying at someone else’s hands. But Nero was effectively forced to commit suicide, in so far as he would have been killed/executed if he hand’t committed suicide.

          Nero is probably the best example of that, though. For example, Otho’s suicide is generally interpreted as an attempt to steer the Romans away from civil war. But Gordian committed suicide after losing a battle, and I suppose it’s likely he would have been executed if he hadn’t. It’s unclear whether Maximian’s suicide was forced, but certainly he had lost by that point. Quintillus, whom I already mentioned, might have committed suicide or might have been murdered.

          There were also a number who were forcibly removed from power without actually being killed. During the Byzantine time period, some were forced to retire to monasteries. For example, John VI Kantakouzenos was forced to retire to a monastery, where he spent the remainder of his life as a monk and historian. He lived a perfectly long life though, dying at the age of 90 or 91. There were also some mutilations, some of which I included, if they apparently resulted in death. (Mutilation of the face was apparently believed to disqualify one from the throne at some point during Byzantine culture.)

          Lucius Tarquinius Superbus, the last of the Rome’s 7 kings prior to the republic, and the one that gave the term “rex” (king) such a bad name in Rome that Augustus was only able to avoid assassination by tricks of propaganda to avoid looking like a king, was apparently exiled.

        • random person says:

          Harold wrote,

          He had (at least) 2 notable failures pertinent to this blog. He failed to control inflation by price controls

          One could probably write a book about the debasement of Roman currency, the motives of insane emperors like Caligula and Nero and how that played into said debasement, the consequences of the debasement, and failed attempts to control it like Diocletian’s price controls. Someone probably has. Not to mention the military aspect, including the wages demanded by the soldiers and the destruction caused by said soldiers as they made civil war to determine who would be emperor.

          More recently, with respect to a Liberian civil war, in which both the government forces and the rebel faction committed mass murder and rape, and the war leaders were arguing over who would get which government jobs, a pacifist leader remarked, if I recall correctly, “You want us to pay you for killing us?” Remarkably, the pacifists won that war (although only after many people were murdered and/or raped and/or otherwise brutalized), defeating both the government forces and the rebel faction, established a democracy, and elected Africa’s first woman president. The story is told in the documentary “Pray the Devil Back to Hell”.

          One might suppose that the sentiment, “You want us to pay you for killing us?” was probably shared by many civilians in the Roman Empire during various civil wars, not to mention the people subjected to forced labor.

          Someone made an attempt to tally the body count of the Roman Empire here. No doubt the tally is far from complete.

    • Tel says:

      As soon as you have a secret ballot, you automatically ensure there is no single individual who can be guaranteed the right to specify any of the so called “societal rankings”.

      The people counting the votes are not supposed to know who cast each individual vote, and therefore they would not know which vote should be the super powerful vote. Admittedly, in real life quite often there’s ways around that … but for the purpose of Arrow’s Theorem we have a mathematical reality that is presumed to “just work” as advertised.

      There’s other things about Arrow that I’ve never liked. For example, he specifies “no random” … let’s consider me and my wife need to decide where to go out for dinner, so I write my vote on a piece of paper, plus I write an integer. My wife writes her vote on a piece of paper, plus she writes her choice of integer. We show the papers to each other and add up the integers … when the result is an even number we go with whatever my wife wrote, when the result is odd number we go with whatever I wrote. Now that’s not random at all, but Arrow wouldn’t like it, because I’m finding ways to get around his rules.

      Point I’m getting at, is why is that a bad system? I should be able to come up with mutually acceptable agreements for group decision making, and why do Arrow’s rules mean so much anyway?

      His rule about “no strategic voting” is even worse. For example, under the Australian voting system (instant runoff, with preferences generally optional but you must start 1, 2, etc) there are situations where you might prefer “A” and then “C” and then “B” but you know that “A” and “B” are strong contenders while “C” is weak. It’s strategic for some of the otherwise “A” voters to vote [1] for “C” then [2] for “A” then [3] for “B” in order to keep “C” in the race and knock out your strongest opponent “B”.

      This would be strategic voting, and people on the whole accept that it might be a reasonable thing under certain circumstances, although very difficult to coordinate in a way that makes it work. Arrow outlaws such coordinated strategy.

      There’s more examples, in as much as for the US election, the votes for Jo Jorgensen could have gone as preferences to either Trump or Biden, but all the people who decided to vote for Jo did understand they could have voted for the candidates more likely to win, and they chose not to do that. Arrow sees that as strategic voting, but he voters did get to make their decision.

      • Harold says:

        “that is presumed to “just work” as advertised.”
        it is not presumed, it is demonstrated.

        “when the result is an even number we go with whatever my wife wrote, when the result is odd number we go with whatever I wrote. Now that’s not random at all.”

        You are not finding ways to get around his rules and Arrow would have no problem with it, but it would break some of his other criteria.

        If we stipulate that elections should have the following criteria: A, B, C and D. All sound reasonable and intuitively we might expect that such elections would result in an unambiguous social welfare ranking. Arrow showed that this is not possible. If we stick to criteria A,B and C, then D is not possible.

        You are then saying yes, but if we don’t stick to C, then D is possible. That is true, but does not say anything about Arrow’s Theorem.

        You are not getting around his rules because they are not rules. They are criteria that we reasonably think should apply to a fair election. Arrow has also said things about elections outside of his theorem, but these are not the same as his theorem.

        I am interested in the instant run off voting (AV) since we recently had a referendum on that here and turned it down.

        This paper points out the problems with AV, with some examples.

        In this case, it appears the vote was split between VFU and NAT. The ALP won most first preferences, but more than 50% preferred either VFU or NAT to ALP. This probably makes sense to you, but they are just initials to me. the eventual winner was VFU.

        In a first-past-the post election, ALP would have won with the same votes cast. It seems unlikely that the same votes would have been cast. I suspect that people who voted VFU or NAT would have coalesced around one of the candidates to a greater degree, but likely ALP would have won as the opposition vote was split.

        Whilst AV does have problems, it does seem to offer a better representation than first-past-the post. For example, people could vote for IND NAT, knowing that their vote was likely to be transferred to NAT or VFU.

        One problem with AV they point out is that it gives preference to major parties. This is true, but not as much as first-past-the-post.

        The strategic voting seems to be exemplified by “how to vote” cards. I presume these are designed to apportion the second choice votes in a way most favorable to the preferred candidate. These obviously undermine the idea of expressing a personal preference, but seems unavoidable.

        • Tel says:

          In this case, it appears the vote was split between VFU and NAT. The ALP won most first preferences, but more than 50% preferred either VFU or NAT to ALP. This probably makes sense to you, but they are just initials to me. the eventual winner was VFU.

          It makes perfect sense … the ALP in 1918 were the militant political arm of the labour union movement, pushing for higher wages, shorter hours and a lot of perks.

          The VFU was the Victorian Farmer’s Union who were generally farm owners who wanted to hire workers and who would regularly lose money when yet another dockyard strike left them unable to ship their produce.

          The National Party claimed to represent all the farming communities but mostly leaned in favour of the VFU and against the ALP. Since there was also Coldham (nominally independent, but mostly in agreement with the National Party) all of those farmer votes stacked up against the labour unions. Which is exactly what should happen.

          That’s the system working properly.

          • Harold says:

            ” Which is exactly what should happen.

            That’s the system working properly.”

            I am inclined to agree.

            It appears to me that the “farmers” were in the majority, but their vote was split. It seems fair that their broad majority view prevailed.

            I do not think that would happen in a first past the post election. It would have only taken a small split between 2 farmer parties for the consolidated labour vote to prevail.

            It thus seems that AV gives a more representative outcome than FPTP.

            Do you agree?

            • Tel says:

              As an Australian who grew up with our system of voting I think it’s a pretty good system, all things considered.

              However, voters behave differently in first past the post systems, and tend to put more effort into the primary elections in order to avoid splitting the vote. They like the final race to be down to two horses … or quite near to that. I would regard every US Presidential election as effectively a two horse race (sorry Jo).

              I should point out that both systems can involve strategic voting (i.e. people end up voting for a candidate who is not really their first preference) and that already breaks Arrow’s rules. People adapt to what they have available, and that’s an entirely reasonable thing to do. One problem with the Australian system is that many people find it difficult to figure out how it works and what they should do, but those people adapt by following exactly the party lines of their chosen party (including all their preferences) … that’s also reasonable if you accept that many people act in a tribally, although I’m not a fan of tribalism.

              For example, in Australia it makes logical sense to strategically put a minor party first … even if you don’t really want them to win, because it sends a message. I often put people like “The Australian Climate Sceptics” as first preference, even though they are a single-issue party with no practical ability to govern. My vote still has full strength when it flows to second and third preference so there’s no loss to me in terms of election outcome … and my first preference gets counted and published which upsets the major parties.

              Doing that sort of thing supposedly exposes an imperfection in the system … but IMHO more people should work the system like that. It’s a legitimate way of expressing concern over issues.

              • Harold says:

                I like the AV system in part because it does allow you to express an interest in minor parties. Vey few vote for them in a FPTP election, but maybe there are many more people who like them than you think. AV does at least allow you to guage that to some extent.

                For example, I wonder how many votes Jo would have got in an AV election.

                When peple vote they are rationally interested in electing their preferred candidate, so yes, people are going to vote tactically and we should ex[pect nothing else. The design of the election will alter how those tactics play out.

        • random person says:

          They are criteria that we reasonably think should apply to a fair election.

          Who is we and what if some of us don’t think all these criteria are all that important?

          What if some of us are less concerned about whether the election is mathematically fair, and more concerned with what some might consider to be more practical matters, such as Rudolph Rummel and Michael Mann’s debate about whether democracy reduces or increases the risk of genocide (and other atrocities)?

          What about democratic methods that focus more on conversation rather than elections? Admittedly, this probably doesn’t scale so well to large numbers of people, but consider juries. Admittedly, there are different procedures for selecting juries, but still, it’s generally considered a more democratic way of determining guilt or innocence in a criminal trial than simply having professional judges. But we also don’t have the entire people of a country (the US, the UK, Australia) or whatever vote on the outcome of the criminal trial. Instead there is… trial by jury.

          Trials by jury do not attempt to “aggregate group preferences”, even of the selected jurors. Instead, either unanimity or a supermajority (rules vary), is required to reach a guilty verdict. And the idea is for them to talk, sometimes a great deal, before voting on a verdict. Hung juries result in a mistrial, and so on. Because “aggregating group preferences” isn’t really the goal; at most, it’s a means to and end: trying to maximize the chances of arriving at as just a verdict as possible, given that human limitations make it impossible to guarantee a just verdict. Opinions may vary, of course, about whether juries successfully achieve this goal..

          • Harold says:

            “Who is we and what if some of us don’t think all these criteria are all that important?”

            My language was clumsy. the criteria appear reasonable to me, but perhaps you don’t agree. Which do you think are not reasonable?

            From Stanford encyclopedia of philosopjy: “Arrow himself took them to be questionable “value judgments” that “express the doctrines of citizens’ sovereignty and rationality in a very general form”

            These are always open to debate, but it is helpful to understand which criterion may be viewed as not required.

            For juries “Because “aggregating group preferences” isn’t really the goal;” means that Arrow’s Theorem is not relevant.

            We must not overstate Arrow. His result is elegant, counter intuitive and informative. It is also relatively easy to understand, compared to say General Relativity. Not that I would put those in the same box (with or without a cat).

            Extrapolating Arrow to draw broad conclusions about democracy does not make sense, but it is useful to incorporate his insight into our understanding of democracy. If nothing else, it allows us to avoid wasting time trying to invent a perfect ordinal voting system. It also requires us to consider the criteria and to think about why we might not agree with them.

            • random person says:

              My language was clumsy. the criteria appear reasonable to me, but perhaps you don’t agree. Which do you think are not reasonable?

              Earlier you listed “It must deterministically provide the same ranking each time voters’ preferences are presented the same way” as one of the criteria. I don’t think that’s a reasonable criteria. We don’t live in a deterministic universe. Trying to eliminate chaos from any system of government (or anarchy) is not a reasonable goal to try to achieve.

              I’m not convinced that independence from irrelevant alternatives is all that important either.

              Perhaps I feel that the most important criteria is how closely the democracy in question ends up resembling a just society — recognizing that, human limitations being what they are, no society will be perfectly just, but, if such things could be quantified, that a 20% just society would be better than a 10% just society. (And also recognizing that such things can’t actually be quantified.) And, looking for significant markers of how just or unjust a society is, we might consider markers such as genocide, forced labor, torture, etc, as indicators of an extremely unjust society, and the lesser presence or absence of such markers as indicators as a less unjust society. Ultimately, this examination isn’t something you do with mathematical precision; it’s something that requires a detailed overview of historical and current events — recognizing that, because some coverups take time to be uncovered, examining history might lead to greater accuracy than examining current events.

              • random person says:

                That is to say, if Rummel should prove to be right, and detailed historical analysis should lead to the conclusion that democracy at least mitigates the risk of genocide, then maybe I should conclude that democracy does work, at least in so far as it mitigates the risk of genocide, which is an important goal.

                On the other hand, if detailed historical analysis should prove Mann right, and show that democracy increases the risk of genocide, then perhaps, based on that, I should conclude that democracy doesn’t work.

                History being what is is, the answer could end up being quite a bit more complicated: perhaps certain types of democracy mitigate the risk of genocide, and other types of democracy increase the risk of genocide. Or perhaps there are other variables that are more significant than the degree of democracy.

              • Harold says:

                I thought it odd that Michael Mann was stepping outside his more usual climate controversies into this debate, but I see it is a different Michael Mann.

                He claims that ethnic cleansing and genocide are modern phenomena. On the surface this seems odd given such masssacres as perpetrated by Gengis Khan at merv and Nishapur. It seems that Mann does not count these as genocide by his definitions as they were not ethnically motivated.

                My initial thoughts are that the link between democracy and genocide is partly correlation rather than causation and is possibly more due to colonisation than democracy. My thoughts are merely speculations.

                Democracy is not a panacea, but nor is it the source of genocide.

              • random person says:

                I’m not sure yet and have mostly only concluded that the matter is worthy of future study. And that it’s a much more significant criteria by which to judge democracy than the question of mathematical fairness.

                I’m also not convinced that it’s appropriate to disqualify mass killings that were not ethnically motivated. While it is interesting if different societal structures tend to lead towards different motivations for mass killings, this does not make mass killings for the sake of money any less historically important than mass killings over ethnicity. Just like when we attempt to solve an individual murder, investigating the motive is part of that, but if the motive turns out to be “inheritance” rather than “racial hatred”, that doesn’t mean that it’s not still murder.

              • Harold says:

                My ill-formed thought on Mann was that in order to make the case that democracy was the cause, he had to differentiate between such historical slaughters. From my very little reading it appears he did make such a case.

                In the case of Genghis khan I think it was a way to win wars. If he killed all the people without mercy in cities that did not surrender but let most people live and go about their lives in cities that did surrender, they would be more likely to surrender.

              • random person says:

                Except that a cursory look at Mongol history reveals that they did have some form of democracy, so the Mongol’s might not be a great example of a non-democratic people who committed genocide (or democide, a term some people prefer when talking about genocidal-scale killings not motivated by ethnic differences).

                Of course, it would take more than a cursory look to go into the type and degree of Mongolian democracy, and whether it had anything to do with their democides.

  4. Harold says:

    Another thought on Arrow. He was producing a social ordering of preferences from individual ordering. In most elections, we only care about the winner. It would not matter if the social ordering got number 12 and 13 swapped, only that it gets number 1 to represent to “social poreference”

    Does this make any difference to the analysis?

    My intuition says that it does not, because any of the orders could be not represented, including number 1. However, intuition is not reliable. Can we derive a voting system that could elect number 1 only and adhere to Arrows criteria?

  5. random person says:

    Looking at Mann further, I think he’s on to something, but it’s hard to follow him because of the terminology he uses. Also, he has a tendency to make some rather broad generalizations, and then admit that his generalizations are not scientific laws and there are exceptions to them. And he’s clearly much more knowledgeable on some aspects of history, than on certain other aspects of history. I get the impression that, while he is quite knowledgeable on ethnic cleansing, his knowledge on the topic of forced labor, for example, is quite weak.

    But the problem of confusing terminology in this field isn’t only a problem when reading Mann. The legal definition of genocide is extremely weak, much weaker than what was intended Raphael Lemkin, the man who coined the term genocide. For example, Raphael Lempkin’s papers apparently included 100 pages on the case of the Belgian Congo (and I’m guessing he included King Leopold II’s rule, before Belgium as a country technically took over), but, if we are to strictly stick to the international legal definition, it doesn’t actually qualify as a genocide, even though an estimated 10 million people, half the country’s population, were killed under King Leopold II and the immediate aftermath of his rule.

    In “Worse than War: Genocide, Eliminationism, and the Ongoing Assault on Humanity”, Daniel Johnah Goldhagen, who is critical of the offical legal definition of genocide, writes,

    Most severe and ridiculous are the definitional problems. The convention does not cover groups slaughtered for political reasons or as economic targets. It prohibits the mass murder of only “national, ethnical, racial or religious” groups. The Soviet Union insisted upon this exclusion because, even as it was negotiating the convention’s terms, its gulag was still fully operational. The consequence of this definitional omission has been even more catastrophic than it first appears. It allows any mass-murdering regime to claim it is engaged in a political struggle. The UN members wanting cover for their inaction can similarly pretend that mass murder’s victims are not national, ethnic, religious, or racial groups but political ones.

    Even more problematic is the genocide convention’s failure to define genocide, let alone include objective criteria (such as a threshold number of people killed) that allow the international community to readily identify genocide while it is happening. This permits the world’s countries to pretend that genocide is not being perpetrated when by any reasonable definition it is. In genocide after genocide, the countries that should have invoked the genocide convention circumvented compliance with its provisions by refusing to utter the word “genocide.” The United States did this in Rwanda, explicitly refusing, in full awareness of the actual events, to call the Hutu’s all-out slaughter of the Tutsi genocide. The United Nations has yet to declare the Sudanese regime’s ongoing genocide in Darfur “genocide.” Only long after any reasonable threshold of genocide had been crossed did the American government, in September 2004, finally use the word “genocide”—and yet the Americans nevertheless failed to urge forceful, effective intervention, and even worked to ensure that the United Nations would not adopt language suggesting that intervention is necessary and obligatory.

    As much as all this robs the genocide convention of meaning and force, there is an even more crippling aspect of the definition of the phenomenon it purports to outlaw. The convention is clearly meant and has been taken to mean only enormous mass slaughters of hundreds of thousands, or millions of people. So a regime may slaughter twenty thousand to forty thousand people—as Hafez al-Assad’s Baathist regime did in Syria—without the principal convention that purports to combat the enormous world problem of mass murder outlawing it. Indeed, the Syrian regime essentially had international immunity for leveling a good part of Hama and wantonly slaughtering its inhabitants. Or a regime that, over decades, murders a few hundred thousand people—as Saddam Hussein’s Baathist regime did in Iraq—is not considered to violate this convention or trigger its provisions. Most mass murders do not, according to the convention’s definition of genocide, qualify for international intervention. The de facto consequence of the convention, the United Nations’ constitution and inaction, and international law has been to sanction a political leadership murdering five thousand or even fifty thousand of its country’s people (particularly if done not too ostentatiously). The international community or some of its members may say that such political leaders are very, very bad people and eventually seek to put some of them on trial. But military intervention to stop the mass murdering would be without a legal foundation and therefore criminal.

    Another grave problem plaguing the genocide convention is its failure to treat genocide—more properly mass murder—as part of a continuum of eliminationist politics. Hence, “ethnic cleansing”—expelling huge populations while murdering “only” a small percentage totaling many thousands—does not fall under the genocide convention. Intervention is not triggered. NATO’s interventions in the former Yugoslavia, first in Bosnia and then in Kosovo, came much too late, after the perpetrators had victimized millions. When NATO finally did act, owing to mounting domestic pressure in Western countries and the desire to make sure the situation did not spin utterly out of control, NATO was without UN authorization and without the genocide convention’s having been invoked. Indeed, international legal experts deemed NATO’s belated intervention illegal because it lacked a basis in international law for outsiders to stop the Serbs from brutalizing, torturing, and expelling Bosnians and Kosovars from their homes and country, and murdering them. If you, as a political leader, want to attack people for whatever reason (they oppose you, you consider them evil, you want to transform the country), then the international community, represented by the United Nations and its powerful countries, tells you that as long as you drive most of them from their homes, even if you kill thousands, for legal and political reasons you will not lawfully face international intervention.

    As if all this is not debilitating enough for establishing an intervention regime that might work against mass murder and eliminations, the convention’s Article II defines genocide as the “intent to destroy, in whole or in part, a national, ethnical, racial or religious group” (my emphasis). The convention’s crafters included the word “intent” as an artful and catastrophic dodge of the problem. A regime slaughtering hundreds of thousands can allege that it is an anti-insurgency campaign’s collateral damage, or famine’s unfortunate consequence, even if the regime willfully causes or fails to alleviate the famine. It can maintain it has never intended to destroy one of the designated kinds of groups. According to the convention, such acts are not genocide. (As I was composing this section, the United Nations issued its disgraceful report that the Sudanese government’s colossal eliminationist and murderous assault in Darfur is not genocide and therefore does not qualify, under the genocide convention, for intervention.) A regime fighting an insurgency that withholds food from a famine-ridden region can claim that the insurgency itself is preventing the food delivery and thus avoid international intervention because no intent to kill through starvation can be proven. Without a mass-murdering regime’s secret records, it is almost always impossible to meet a legal threshold of proving intent. This makes it all but impossible for the United Nations to establish a legal finding of genocide while mass murder is under way, while acting against the murderers and saving lives is possible.

    In his own writing, Daniel Jonah Goldhagen makes it clear he thinks the term “genocide” should be defined more broadly than it is defined by international law, and I believe this is consistent with the intent of Raphael Lemkin, the man who coined the term. Daniel Jonah Goldhagen also uses the term “eliminationist” to discuss related policies which do not fit even into his expanded definition of the term genocide. Perhaps because he doesn’t wish to offend people who are attached to the legal definition too much, he doesn’t always specify whether he considers a particular eliminationist assault to be genocide or not.

    Michael Mann also recognizes that the international legal definition of “genocide” is too limiting to discuss all he wishes to discuss, but takes a different approach to the problem, making a table with a bunch of different terms in it, such as classicide, politicide, etc, and shading in certain parts of the table that he believes qualify as what he class “ethnic cleansing”. Subsequently, there’s a lot of times in his text when he says things like, such and such wasn’t genocide, it was politicide. I really feel like it is much better and less confusing to use an expanded definition of the term genocide, as Goldhagen does, rather than nitpicking on whether a particular mass murder should be called genocide, politicide, or whatever. (Especially since leaders may lie about their motives for killing people anyway. For example, the perpetrators of the Guatemalan genocide claimed to be going after communists, but it seems implausible to think that children too young to even understand what communism is could be communists.)

    However, in spite of the limitations of Michael Mann’s work, the confusion I feel in following his wording, his lack of knowledge on certain topics such as forced labor, I do feel like he is on to something. For example, on page 502 of “The Dark Side of Democracy: Explaining Ethnic Cleansing”, he writes, ““The people” came to have a dual meaning – as the demos of democracy and as the ethnos or ethnic group. Modern ethnic cleansing is the dark side of democracy when ethnonationalist movements claim the state for their own ethnos, which they initially intend to constitute as a democracy, but then they seek to exclude and cleanse others.” There is an unfortunate tendency for many democracies (or would-be democracies, or republics with elements of democracy, or whatever) to adopt a rather limiting concept of rule by “the people” which excludes a lot of other people. I honestly think Mann could take this much farther than he does if he knew more about Roman history, for example, or if he considered the way the United States has often behaved towards foreign nationals.

    • random person says:

      The part starting from, “Most severe and ridiculous are the definitional problems,” and ending with, “This makes it all but impossible for the United Nations to establish a legal finding of genocide while mass murder is under way, while acting against the murderers and saving lives is possible,” was meant to be in a blockquote.

    • Harold says:

      I think one point is that we should not consider mass murder less abhorent whether or not it fits a specific definition of genocide. I hope we can agree that slaughtering the entire population of a city (as Gengis Khan, or indeed the bible) is abhorent, whether otr not it is genocide.

      • random person says:

        Yes, and I think Michael Mann would agree too. It would just be easier to read his book if he had picked some suitably broad term he felt comfortable with, such as “mass murder” or whatever, and got on with his analysis, rather than going on so much about which particular label should be put on which mass murder.

        It’s a shame that so many in the United Nations apparently don’t agree.

      • random person says:

        However, I would like to state for the record that I agree with Raphael Lemkin that what King Leopold II did in the Congo was a genocide, regardless of the UN definition.

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