25
Apr
2018
Potpourri
Some of these may be duplicates; I have had a hard time keeping up with stuff lately…
==> My latest IER post tackles Krugman’s misleadings claims on renewables. Some pretty graphs!
==> A funny comic on Rothbard, Rand, and Marx.
==> I don’t know how long these have been available, but check out audio clips from Mises!!
==> The only kind of government intervention I support.
==> Contra Krugman 132 goes after the Phillips Curve. Ep 133 is on protectionism (a fun audio clip). Ep 134 has lots of good banter, with some occasional discussion of Krugman to boot. Ep 135 is about renewable energy.
==> My EconLib article on the “power” of statistical tests.
==> David Gordon remembers the recently deceased Leland Yeager, and what Yeager learned from Mises.
I love Existential Comics. The very first one is well worth a look, it deals with ideas about identity. The D&D ones are also very funny.
Gastrodiplomacy is great for Thai food. it cannot be the whole explanation, since he says he grew up with Thai food and he went to college in 2008, meaning he grew up on the 1990’s before the gastrodiplomacy initiative started in 2001. WHilst this does explain some of the apparent excess of Thai restaurants, they were still over-represented before this policy.
Existential Comics is garbage; the author even more so. Check his twitter; the only thing you’ll be impressed by is his stupidity (and I do not say this with any lightness or transience of purpose).
I agree. I have never seen such a defender of communism. He claims capitalism has killed more than communism. Regardless, the comics are pretty funny sometimes and I almost always learn something.
I dislike the comics, too. I find them bizarre and boring.
The drawing style’s also bad.
Learning about cartoonists can be a bad thing. I can never view Dilbert in quite the same way since Adams lost his mind. Perhaps a bit like watching sausages and laws being made.
Harold wrote: Learning about cartoonists can be a bad thing. I can never view Dilbert in quite the same way since Adams lost his mind. Perhaps a bit like watching sausages and laws being made.
Harold, if someone said, “I can’t watch Ocean’s 11 after seeing Clooney lose his mind by endorsing Obama” what would you think of someone like that?
Adams hasn’t lost his mind. He’s just being contrarian.
Adams kind of supported Trump, the lefty code word is “lost his mind”.
I go and study this political stuff so you don’t have to.
It is not because he supported Trump that I say he has lost his mind. It is more because he says he is not supporting Trump and is merely making disinterested observations when he is clearly viewing everything he writes through a pro-trump filter. All the while talking about confirmation bias. I think he started off just commenting about how trump would be more successful than everyone predicted, and he was certainly right about that, but somewhere along the way he got sucked in to being an advocate.
E Harding wrote: “Existential Comics is garbage; the author even more so. Check his twitter;”
So Harold can’t like Dilbert because Adams endorsed Trump, and you can’t like a funny comic because the author is a commie.
I did not say I could not like Dilbert, I said I can never view Dilbert in quite the same way. I still enjoy Dilbert cartoons.
The comic isn’t funny! It’s dumb!
Can you or should you enjoy a Woody Allen movie or a Roman Polanski movie (Allen is a pedophile because he married his exwife’s adopted daughter that he helped raise and Polanski is wanted for rape in the US)? Do we care what the assembling line worker who produced our vehicle or the farm worker or rancher who produced our food does with their income or who they are?
I tend to judge the art and not the artist. I know in my work I do not want to have to pass a political litmus test every time I go to work. I try not to impose that on others. There are limits, there are dangerous people that I simply avoid and there are some companies I do not patronize. I think the civil rights bus boycotts made sense.
I am shocked by Existential’s defense of Stalin and Lenin, but he still makes me laugh and think.
I don’t see eye to eye on everything Dr. Bob does either but I enjoy his insights and he makes me think and I thank him and pay for his work. I do not think I would pay for Existential’s work.
Harold liking Existential Comics is evidence of a well ordered and rational universe.
It could also be evidence to God’s plan to create a well ordered and rational universe but with a sample size of one universe we could be facing a “replication crisis” if I attempt to make any assertion about God.
Great article on significance and power. This explains it very clearly. I am not sure about the magnitude part.
“In other words, there will be an entire literature consisting of papers finding statistically significant evidence that the coins are unfair, in which the “best guess” is that the coins come up Heads all the time and never come up Tails.”
Wouldn’t it be the case that each article simply accepts or rejects the null hypothesis? I can see that the published literature will overestimate the magnitude through publication bias . Most people who find no result simply will not publish, only those that find a significant result. There is an massive under-reporting of negative results, which is a shame. Is this the source of the magnitude error, or is there something else that I have missed?
There is a movement in clinical trials to publicly announce the trials and the objectives before the study is done. This allows the extent of negative results to be assessed and also prevents selecting sub-sets where significant results can be found. For example, no effect is seen in all people, or all women, or all women over 50 but there is an significant effect for black women over 50. If we have a 5% threshold and we can find 20 different sub-categories we have a very good chance of finding an apparently significant effect by chance.
Harold wrote: “Wouldn’t it be the case that each article simply accepts or rejects the null hypothesis? I can see that the published literature will overestimate the magnitude through publication bias . Most people who find no result simply will not publish, only those that find a significant result. There is an massive under-reporting of negative results, which is a shame. Is this the source of the magnitude error, or is there something else that I have missed?”
You’re missing something, Harold. Statistical papers don’t simply report, “We reject the null.” They also report the estimated value of the parameter.
And so, in the contrived setup I gave in the article, they would have no choice but to report that the coin came up Heads 100% of the time, because those are the only sample runs that would count as statistically significant (with the smaller sample size).
This is a subtle yet very important point and I always think learning more about statistics can never be a bad thing, so I am grateful for any help in understanding this.
The experiment was to test for a biased coin. The magnitude of the effect is the extent to which the coin is actually biased. The null hypothesis was the coin was not biased. They report that the coin came up heads 100% of the time which is enough to reject the null hypothesis at 95% confidence.
What would they report as the magnitude of the parameter, or the real extent of bias? It does not seem sensible that they would report the coin is 100% biased, i.e.a two headed coin, although that was the result they got.
So whilst it is entirely reasonable to report that they got 100% heads, that is not the same as them saying that the coin was two-headed and any such claim would surely be rejected before publication. After all, by the experimental design they acknowledge there is a 1 in 20 chance the coin is not biased at all, so to estimate the extent of bias at 100% makes little sense. I do not know how they would set about estimating the magnitude of the bias.
How do they arrive at the estimated value if the parameter, and can you explain what this would be in one of your coin examples? Or perhaps point me to a source?
Harold wrote: “What would they report as the magnitude of the parameter, or the real extent of bias? It does not seem sensible that they would report the coin is 100% biased, i.e.a two headed coin, although that was the result they got.”
I get what you’re saying, Harold, and yeah maybe we’d hope that the author, the referees, the editor, and all readers of the journal would take the reported result with a grain of salt. But nonetheless, when you do a regression in a journal article and report your results for the variables of interest, you report your estimate of the true mean as the sample mean. So if your threshold for “statistical significance” means that you can only send in a result when the sample showed you getting 100% heads, what else could you report for your estimate of the likelihood of heads, except “100%”? That’s what turned up in your sample. It would be arbitrary for you to say some other number.
If researchers look at Seattle teenage employment after a minimum wage hike and find it went down 0.1%, what else could they do except say their best guess of the true impact is negative 0.1%? Yes they could build a confidence interval around it, but if they had to pick a number they’d pick their sample mean, right?
But does this not come down to publication bias?
I think we have no option, as you say, but to use the published means as the best estimate for the population mean.
However, if all studies were reported, we would get the one with 100% heads, but we would also get the one with 50% heads, showing no bias even if there were an actual bias. If we picked a study at random we would be as likely to underestimate as over estimate. Since the underestimate is not likely to be published we are only ever going to find the over-estimate.
Perhaps we are not disagreeing, as the end result will be a finding of an exaggerated magnitude, so there is certainly a problem.
Journals are not interested in publishing articles that say “I had an idea that something may show an effect, but when I looked I didn’t find one”. That is probably because readers are not interested in reading them either.
Once the cat is out of the bag, we often do get negative findings published but only if the finding attracts particular interest. We can hope that these errors will self correct eventually if an area attracts sufficient interest.
Harold wrote: “But does this not come down to publication bias?”
I just looked up the Wikipedia discussion and yes, the effect I’m talking about is something they included under that term.
There is a more extensive discussion in the book Statistics Done Wrong.
Oh yeah, Tom Woods #1142 and Arrow’s Impossibility Theorem, those are not very weak conditions. Arrow’s concept of “dictator” doesn’t mean what most people think of a dictator to mean and it certainly does NOT mean one person who always gets his way.
Think about this, you have a referendum and 50 people vote YES but only 49 people vote NO, and we presume secret ballot and simultaneous voting. So the YES wins by one vote, and who exactly was the dictator?
If you think the presumption of simultaneous voting is unreasonable, then OK we have non-simultaneous voting so Arrow would say the very last person who voted YES would be the “dictator” but this guy has no idea at the time he voted that his vote would be pivotal (nor does anyone else have any idea until the votes are counted). How does this person “always get his way” when the next vote might be completely different? Clearly he got his way this time around, and so did 49 other people.
Besides that, when was the last recorded vote on any national scale that was decided by a single vote?
Arrow’s theorem is a trick!
Linky because Bob didn’t include it in the Potpourri list…
https://tomwoods.com/ep-1142-why-does-politics-yield-perverse-outcomes-again-and-again/
Tel, the non-dictator is actually an extremely weak condition. It does not say that the social preference ordering is not allowed to match some individual’s preference ordering in some particular case. If there’s a 49-49 tie and a voting method allowed the last person to break the tie and determine the outcome, that would NOT contradict the non-dictatorship condition. It’s not enough for a person to get his way in SOME scenario, the non-dictatorship condition is about a person getting his way in ALL scenarios, regardless of whether it’s a tie or not. That’s what makes Arrow’s theorem so surprising.
Look at Wikipedia’s formal statement of the theorem. The non-dictatorship condition states “There is no individual, i whose strict preferences always prevail. That is, there is no i ∈ {1, …, N} such that for all (R_1, …, R_N) ∈ L(A)^N, a ranked strictly higher than b by R_i implies a ranked strictly higher than b by F(R1, R2, …, RN), for all a and b.” en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem#Formal_statement_of_the_theorem
Note the sequence of the quantifiers. The condition does not say that for each (R_1, …, R_N), there is no i such that i gets his way in that particular case. There certainly could be different i’s for each list of preference orderings, and that would be fine. But what the condition says is that there is no SINGLE i such that for ALL possible sets of preference orderings, i gets his way in all of them.
This is newly discovered footage of Tel critiquing Arrow’s Impossibility Theorem.
Tel wrote: Oh yeah, Tom Woods #1142 and Arrow’s Impossibility Theorem, those are not very weak conditions. Arrow’s concept of “dictator” doesn’t mean what most people think of a dictator to mean and it certainly does NOT mean one person who always gets his way.
Tel yes it means precisely that. I haven’t listened to my podcast with Tom so it’s possible I said something misleading, but Arrow’s definition of a dictator is quite intuitive, and to say “The social welfare function shouldn’t allow a dictator” is extremely weak.
OK, then answer the question from above: you have 99 people who vote in a referendum, and they all write down their votes in secret on paper ballots, all votes get put in a big box and then the votes are revealed simultaneously and counted. 50 vote for YES and 49 vote for NO so tell me who is the “dictator” and how this person knows they are a dictator at the point where they are voting ?
There’s a theorem for it, right? So you just apply the theorem and it will always identify the dictator.
Also once you have found this person, show the meaningful similarity between their vote and Joseph Stalin, or Mao Zedong, or Pol Pot who are actual “dictators” in the correct sense of the word.
Tel, see my comment above. You are misunderstanding what Arrow’s theorem is saying. If you have a 49-49 split and the 99th person breaks the tie, that is NOT an example of “dictatorship” as the word is used in Arrow’s theorem. What dictatorship means in Arrow’s theorem is that is that there is one guy who always gets his way in all scenarios, even when there is no tie. If someone gets his way only when there is a tie, that does not constitute a dictator in Arrow’s theorem,
If votes are revealed simultaneously there is no 99th person, nor is there any first, second or third.
That’s the normal kind of dictator, with the riding boots and the peaked cap.
But such a person simply does not exist in a democratic system, which is easy to prove. Suppose person “X” is determined as the supposed dictator in this particular election (I don’t care how you want to determine that, but you must have some method to find the dictator else you cannot say there is one), and then next election every other person votes opposite to person “X”… well now the “dictator” does not get his way anymore. Thus, the dictator does not reliably get his way in every scenario.
Of course one person might happen to get his/her way in many scenarios, but there’s no guarantee of that, nor is there any way for the individual to create circumstance to generate a guarantee. If one person could generate a guarantee of getting their way, then every person would do whatever that person is doing.
Tel, no one is claiming that democracy is a dictatorship. What Arrow’s theorem says is that IF a voting method meets certain criteria, THEN it must be a dictatorship. Another way of phrasing that is that all non-dictatorial systems violate one or more of those other criteria.
And just so you know, Arrow’s theorem only works when voters have at least three options to choose from. Your example only involves “yes” and “no”. So Arrow’s theorem doesn’t apply here. If voters only have two options to choose from, then majority rule actually satisfies all the ideal properties that Arrow’s theorem says are impossible to satisfy when you have 3 or more options.
It’s a bit more complex but you can easily think of a three-way scenario, and since you don’t even believe a tie is necessary then I can come up with something like this:
100 people vote and there’s three candidates. They write down their preference in secret and the paper ballots go into a box, after which all are simultaneously revealed.
60 people vote A, B, C
30 people vote B, C, A
10 people vote C, A, B
A wins by outright majority.
Who is the “dictator” or for that matter who is the “pivotal voter” as identified in the theorem?
Tel, Arrow’s theorem requires you to not just declare a winner, but to declare a social preference ordering. So are you saying A, B, C wins or are you saying A, C, B wins? And what method are you using to determine that?
By the way, here is a simple proof of Arrow’s theorem: http://www.thebigquestions.com/2010/10/26/straight-arrow/
There’s three candidates: “A”, “B”, and “C”.
Candidate “A” wins by a majority so therefore candidates “B” and “C” are losers and do not win the office.
That’s got to be the most confusing explanation I have ever seen. The pizza shop always requires a first, second, and third preference in case they run out of something? Are you kidding?!? Find a proper pizza shop that sells what you ask for.
Then he shows a voting pattern that is a perfect three-way tie and says that somehow Alice wins. Well that’s just not normal when people think about how voting works. The probability of getting a perfect tie on all preferences is astronomically small if you have even a few hundred people… but if you ever did get a perfect tie you would not be able to declare a winner.
As I commented on Landsburg’s post
“I remember someone stating something like the only fair voting system ends up appointing a dictator. This is not the case, as it states there is no fair voting system that can satisfy all three axioms. There is no particular reason to pick the dictator one as “special”.”
To which he replied
“Arrow’s theorem says “No social welfare function satisfies Axioms 1, 2 and 3.” My preferred statement is “Any social welfare function satisfying Axioms 1 and 2 must violate Axiom 3.” Of course, one could permute the 1,2, and 3 in any way one wanted to get other equivalent statements. But I’ve found that it’s a little easier — for me at least — to get the ideas across when I state it my preferred way.”
I think this discussion illustrates the problems of viewing the “dictator” axiom as the subject.
Tel wrote: “OK, then answer the question from above: you have 99 people who vote in a referendum, and they all write down their votes in secret on paper ballots, all votes get put in a big box and then the votes are revealed simultaneously and counted. 50 vote for YES and 49 vote for NO so tell me who is the “dictator” and how this person knows they are a dictator at the point where they are voting ?
There’s a theorem for it, right? So you just apply the theorem and it will always identify the dictator.”
Tel, it’s as if Keshav and I said, “The Pythagorean theorem proves that for any right triangle, a^2+b^2=c^2,” then you say in indignation, “Oh? Well here’s a square with sides a and b. Show me the alleged side c. There’s a theorem, right? Idiots.”
I’m not saying you’re dumb, I’m saying you are misunderstanding what Arrow’s theorem is saying. And no, in this case, it’s not merely that the mathematical syntax doesn’t line up with the commonsense usage of the term.
If it helps, let me confess that when I was in grad school, I spent a good 24 hours thinking I had found a counterexample to Arrow’s theorem. But then I realized my mistake.
For your specific example, you’re right, there’s no dictator in that example. Arrow’s theorem doesn’t say, “There’s always a dictator for any social choice rule.” Rather, it says, “For any social choice rule that obeys these other properties, there must be a dictator.”
Specifically, one of the other properties is transitivity. So standard democratic rules fail for that reason. You can arrange people’s preferences such that every individual has transitivity, but nonetheless with majority rule you get “society” preferring A to B, B to C, and yet C to A. This is why Keshav why saying technically, Arrow’s Theorem assumes we are dealing with at least three distinct outcomes over which people (and hence “society”) have preferences.
Just to repeat my initial point, this word “dictator” has a meaning, and it’s attached to some pretty strong emotional connotations.
So the idea of a referendum would probably be the most widely used and simplest configuration for a vote to settle some question in society. If Arrow doesn’t apply to that then we can put a pretty big asterisk on the box right there.
But I would take a step further and say when you look at the 2016 US presidential elections, although there were nominally three candidates, it was also structurally the same a simple YES / NO referendum because there really were only two viable candidates. Gary Johnson never had a chance of winning in 2016. Sure Johnson got 3.3% of the vote, and that was an achievement for a Libertarian, but those were all protest votes sending a message that they hated the major parties. So basically Arrow does not apply to US presidential elections either. That’s a second asterisk on the box, and remember we are talking about “dictators” here.
But what does that mean in practice? Sometimes the voting rules will fail to correctly determine the rank order of the losers. So in the US 2016 presidential election, do you have a sneaking suspicion that Gary Johnson really deep down beat Hillery and the voting system just ripped him off? Probably not, right. You can just see at a glance that Johnson came third (i.e. last).
OK, let’s just suppose somehow there was a way to prove the weaker condition that the second and third places are poorly defined and therefore no clear decision can be made there. It still doesn’t produce a “dictator” in the way that if you grab a few people on the street (in the style of Mark Dice) and you ask, “Did you see the dictator in the 2016 election?” and they will answer something like, “Yeah Trump is LITERALLY HITLER!!!” and you explain, “No no I’m not talking about Trump, he was a clear winner, I mean the way Gary Johnson came third, but he might actually have come second and it’s all because of the preferences of some person I cannot even name, and our rotten voting system.”
If you try that what’s going to happen is people will back away slowly and signal to their friends to call the cops, because a crazy man is on the loose.
After the Superbowl, do you hear a lot of commentators bemoaning the way the rank of all the losing teams might not be fairly treated under NFL rules? Do you hear that in any sport? They generally talk about the winning team.
Using the word “dictator” does not apply, nor is there any one person who can reliably always decide the outcome of any real world election. All Arrow offers is some hypothetical circumstances where perhaps one person’s vote counted more than it ideally should somewhere down the rank of preferences for candidates who didn’t win anyway… even then it doesn’t reliably happen in every election it requires a certain pivotal voter, and even on those occasions when the pivotal voter does exist the structure of the secret ballot ensures no one can identify this “dictator”, not even the man himself.
This is literally NOT Hitler, and going down that path of using emotive words like “dictator” is what the “Progressives” do for attention seeking. We are better than that.
In fact, I challenge you to find any real world election and point out the “dictator” who was able to control the outcome. Seriously, pick any public well known election, from any country, anywhere in the world in the last 100 years and explain the relevance of Arrow’s theorem to that particular election (including an identification of the “dictator” and what this nefarious commandant did to dictate the outcome).
Tel, unfortunately you’re completely misunderstanding Arrow’s theorem. Let me go through your points anyway though:
“It still doesn’t produce a “dictator” in the way that if you grab a few people on the street (in the style of Mark Dice) and you ask, “Did you see the dictator in the 2016 election?” and they will answer something like, “Yeah Trump is LITERALLY HITLER!!!” and you explain, “No no I’m not talking about Trump, he was a clear winner, I mean the way Gary Johnson came third, but he might actually have come second and it’s all because of the preferences of some person I cannot even name, and our rotten voting system.”” Tel, no one here is claiming the 2016 election involved a dictator. No one. The claim is that if an election method satisfied certain properties, THEN there would be a dictator. But the election methods in the US do not satisfy those properties, so there isn’t a dictator. That doesn’t mean Arrow’s theorem is useless, it’s actually a theorem with profound real-world consequences, but those consequences do NOT involve identifying dictators in democracy.
“All Arrow offers is some hypothetical circumstances where perhaps one person’s vote counted more than it ideally should somewhere down the rank of preferences for candidates who didn’t win anyway… even then it doesn’t reliably happen in every election it requires a certain pivotal voter, and even on those occasions when the pivotal voter does exist the structure of the secret ballot ensures no one can identify this “dictator”, not even the man himself.” Tel, Arrow’s theorem is NOT talking about some scenario where some guy has more influence than he should. It really is talking about a Hitler-like figure who gets his way in all scenarios, even scenarios where everyone else is against what the dictator wants.
“In fact, I challenge you to find any real world election and point out the “dictator” who was able to control the outcome. Seriously, pick any public well known election, from any country, anywhere in the world in the last 100 years and explain the relevance of Arrow’s theorem to that particular election (including an identification of the “dictator” and what this nefarious commandant did to dictate the outcome).” Again, no one is claiming that there are dictators in real-world elections. I think you’re focusing too much on the dictatorship condition of Arrow’s theorem and ignoring the test of the conditions. What Arrow’s theorem really says is “All non-dictatorial systems are fundamentally flawed.” So the implication that Arrow’s theorem has for real world elections is NOT “there’s a secret dictator no one knows about” but rather “that election was fundamentally flawed”.
On the topic of dictators who always win elections, I thought this was a little bit charming.
https://pbs.twimg.com/media/Db631fGU8AAK5NH.jpg
Really, seriously drop all talk of voting and elections when discussing Arrow. They are just a flashy distraction. The theorem is about ranking preferences. It basically says that if you have everybody rank alternatives then there is no entirely satisfactory way to combine those rankings into a “What the group wants” ranking. There are several desirable conditions you could ask for but it turns out you cannot have them all.
The way the theorem is usually stated, with having a dictator, can be thought of this way. You describe several conditions that are obeyed by *individuals* when ranking alternatives. It turns out that no *divided* authority has those properties,only individuals do. So if your system has those properties then there must be an individual— the dictator— whose preferences are the system’s preferences.
Bob & Keshav
I think a problem Tel is having can be identified this way. Let D be the dictator. The rankings match D’s every wish. But what if D changes his preferences? That is we have a new set of preference lists where only list D is different. It is now D2. Is it necessarily true that the function produces D2, the new preferences of D, or might there now be a different dictator Q?
More simply, D and E swap preference lists. Now E is the dictator. This seems counterintuitive to the usual understanding of dictator.
No, if D and E switch preference lists, D will still be the dictator. I agree that if D and E switched preference lists and the dictator changed, it wouldn’t match the common-sense understanding of dictator. But the dictator doesn’t change. When Arrow’s theorem talks about a dictator, it’s talking about someone whose individual preference ranking doesn’t just match the social preference ranking in one particular case, but in all cases, regardless of how his individual preference ranking changes in different case.
Look again at Wikipedia’s statement of the non-dictatorship condition: “There is no individual, i whose strict preferences always prevail. That is, there is no i ∈ {1, …, N} such that for all (R_1, …, R_N) ∈ L(A)^N, a ranked strictly higher than b by R_i implies a ranked strictly higher than b by F(R1, R2, …, RN), for all a and b.” It’s talking about the notion of a single dictator who is the same guy in all possible sets of preference ranking lists.
So if every single person other than the dictator all gangs up and votes against that dictator, then you think the dictator will still win the election… but how? Do an example with numbers and show me how the one vote of the dictator can be larger than everyone else put together. Just demonstrate any example where this might work.
Tel, no one is claiming that there are dictators in democratic elections. Arrow’s theorem does not say “Democracies are dictatorships.” That would be absurd. If you want an example of a system where the dictator always get his way, it’s called a dictatorship. If Kim Jong Un wants to nuke Seoul and all his people don’t want that, he gets to nuke Seoul.
What Arrow’s theorem says is basically “If a system meets conditions X, Y, and Z, then it must be a dictatorship.” Does that mean democracy is a dictatorship? No, democracy is definitely not a dictatorship. So what Arrow’s theorem is really saying, in the case of democracy, is “democracy doesn’t meet conditions X, Y, and Z.” And that’s a surprising and important fact.
Well democracy clearly DOES meet the unanimity condition (i.e. if everyone votes for exactly the same thing, that’s what we get). So that’s not surprising.
You have just told me that democracy has no dictator, so I presume that condition is met, and there’s only three conditions meaning by elimination democracy fails the transitivity condition meaning you don’t reliably get a full ranking of all the loser positions.
Well most people don’t even care about accurate ranking of the loser positions, and I personally can’t find myself seeing this as a deep flaw in democracy (there are other problems like the majority of people “rationally” wanting to steal from the rich minority but that’s not a flaw in the process of determining the outcome of the vote, especially not a problem with ranking the losers)
But even if people did care, you can still look at most practical situations (e.g. 2016 US elections) and say, OK Hillary came second and Johnson came third. It’s just very obvious in most cases, although perhaps if you search long and hard you can find an ambiguous case.
I remember now there was a Green candidate, Jill Stein who even came in behind Johnson… maybe we can argue about third and fourth place, and then call that a flaw in democracy. The US style of election doesn’t even both asking the voters who they think is second best (Australian elections do ask, but we have no President, I happen to think there’s no problem in Australia either, other than the lack of quality candidates and the occasional missing ballot box).
Our system doesn’t meet the Independence of Irrelevant Alternatives (IIA) condition. We can’t say with certainty who would have won between Bush and Gore if Nader hadn’t been on the ballot. And we know that it is possible that the presence of Nader on the ballot impacted the rank order of Bush and Gore in the final vote totals, even though his presence on the ballot should be irrelevant to the question of whether the US electorate prefers Bush or Gore.
Well the US system obviously does not care who might have won, because it does not even ask the voters for preferences.
The Australian system DOES ask voters for preferences and it can correctly resolve the winner in the case of minor party “spoilers” which we have all the time over here. The Australian system is about 7x more expensive to operate on a per-vote basis (last I checked which was some time ago).
Each system is based on the general agreement of people to use that system, but both systems fail to comply with Arrow’s requirement that all the losers in the election are ranked.
Tel wrote: “So if every single person other than the dictator all gangs up and votes against that dictator, then you think the dictator will still win the election… but how? Do an example with numbers and show me how the one vote of the dictator can be larger than everyone else put together.”
Tel, all I can do at this point is reiterate yet again that you are utterly misunderstanding what the claim is. We keep repeating that a democratic election satisfies the non-dictatorship principle, but fails for other reasons, and yet you keep demanding: “Show me how a democratic election can have a dictator!”
Right Keshav, in all cases. And the preference lists for D and E are exhaustive, covering all possible eventualities. So under the swap I mention there is ex hypothesi a solution where E is dictator.
No Craw, you misunderstand what I meant by all cases. What Arrow’s theorem means by the word dictator is someone whose entire preference list matches the entire social preference list, regardless of what the dictators’ preference list is. That is to say, if you change the dictator’s entire preference list into something completely different, he still remains the dictator. In particular, if you swapped D’s preference list with E’s preference list, D would remain the dictator.
In short, a dictator is someone who gets his way because of who he is, not because of what he wants. That is what makes Arrow’s theorem so surprising.
Craw wrote: “More simply, D and E swap preference lists. Now E is the dictator. This seems counterintuitive to the usual understanding of dictator.”
I’m breaking my rule and responding to Craw (if that is your real name…) for the benefit of onlookers: I can’t tell if you understand the problem in what you are saying and are just trying to help me see what’s tripping up Tel, or if you think you’ve put your finger on a real problem with Arrow.
So, to be clear, I agree with you that if you could just switch who the dictator is, then that would be a weird usage of the word “dictator.” Fortunately for Arrow, that’s not how it works.
If you didn’t realize that, then you don’t understand the proof at all, and you shouldn’t be confidently lecturing Keshav and me on how to discuss it. Have you ever read Sen’s proof?
All voters submit ordinal lists for all possible cases, and a function is defined. The structure of the lists obeys the conditions. Under this arrangement Tel is dictator. Kirk is just a guy.
On another planet in the multiverse we have exactly the same conditions but Tel has Kirk’s lists, Kirk has Tel’s. All of them for every eventuality. Same function. Now Kirk is dictator.
The result of theorem applies to the *lists*. Talking about the voter/person is just an easy shorthand.
So on earth if Tel and Kirk simply swapped lists and we find Kirk is dictator.
If readers head over to wiki they will see L(A) defined as I indicate, all preference orderings.
Here’s the formal definition of non-dictatorial
https://en.m.wikipedia.org/wiki/Non-dictatorship
Scroll down to the Arrow paragraph.
Craw, I’m perfectly fine if you want to say there’s something weird about Arrow’s framework that smuggles things in, but I really think you’re misunderstanding the dictatorship condition. Here’s Wikipedia:
“Non-dictatorship is one of the necessary conditions in Arrow’s impossibility theorem.[1] In Social Choice and Individual Values, Kenneth Arrow defines non-dictatorship as:
There is no voter i in {1, …, n} such that for every set of orderings in the domain of the constitution and every pair of social states x and y, x {\displaystyle P_{i}} P_{i} y implies x P y.”
(The formatting got screwed up; people should follow his link.)
So for example, the social choice rule might be: “Whatever individual 67’s rankings are, make that the social rankings.” So for any possible set of rankings by each member of society from 1, 2, 3, …, 8 billion, we have a definite mapping. It always maps from the set of 8 billion lists into the single list that person #67 had. So he is clearly a dictator, as the definition you cited makes clear.
In particular, suppose individual 67 ranks things “Clinton Trump Nader Craw”. Then the social ranking is “Clinton Trump Nader Craw.”
Now in an alternate universe, individual 67 ranks things “Craw Clinton Nader Trump” while individual 3 ranks them “Clinton Trump Nader Craw” (and hold everybody’s else’s lists the same). I think you are saying the rule will still say “Clinton Trump Nader Craw”–meaning now individual 3 has become the dictator in this universe–but no it won’t. The rule always takes individual 67’s list and makes that “society’s” list.
(You can dress it up and include all 8 billion rankings, but the principle is the same. I’m just saving time in typing.)
There is an easy counterexample to your claim. Let there be a unique voter for each ranking and the rule is
Clinton Trump Nader Craw.
Tel had that list so Tel was dictator. If Tel and Kirk swap lists then Kirk is dictator and Tel is not.
It is Kirk’s list which matches the social choice.
Craw, the rule “individual 67 always gets his way” is an example of a dictatorship. The rule “Clinton Trump Nader Craw always wins” is not an example of a dictatorship. (So it obeys the non-dictatorship criterion of Arrow’s theorem, though it violates other criteria like unanimity.). If there is no single person whose preference list always matches the social preferences list even when you completely alter the person’s preference list, then it’s not a dictator.
Craw, I’m going to start a new post…
Craw, to use your terminology, a dictator for the purpose of Arrow’s theorem is someone who gets his way in all planets in the multiverse, not just a single planet. If a particular rule does not always match the same individual in all planets, then the society is not a dictatorship. Someone who just happens to have his preference list match the social preference list in one particular planet is simply not a dictator.
That’s basically what I’m saying w.r.t. the secret ballot in as much as it forces isolation between the voters and the set of preference counts, and removes the “easy shorthand” leaving only these “lists” as you call them.
It does more than that, because every individual voter lacks knowledge of what every other voter is doing at the time votes are cast thus making it impossible for any individual voter to act on the knowledge, even if somehow that voter did become the “dictator”.
And I still hold that “dictator” as per the Arrow proof is only a possibility under some exceptional circumstances, although I’ve largely given up convincing anyone of that. I guess there’s better things to get on with.
Craw, good question. And here is the answer: if D changes his preference list from D1 to D2, then the function will change from outputting D1 to outputting D2. In other words, the term “dictator” as it’s used in Arrow’s theorem exactly matches the common-sense usage of the term.
That implies that a person can somehow walk into an election with knowledge of Arrow’s theorem and automatically guarantee a win for their chosen candidate.
If that were true then why doesn’t everyone do this? And if everyone can’t do it, then how would you go about identifying the dictator BEFORE the election and maybe ask them nicely not to use this magic (especially difficult when the rules for the election are the same for all voters)?
“That implies that a person can somehow walk into an election with knowledge of Arrow’s theorem and automatically guarantee a win for their chosen candidate.” No, it doesn’t mean that in the slightest.
“If that were true then why doesn’t everyone do this? And if everyone can’t do it, then how would you go about identifying the dictator BEFORE the election and maybe ask them nicely not to use this magic (especially difficult when the rules for the election are the same for all voters)?” Tel, for the millionth time, Arrow’s theorem does NOT say there is a “hidden dictator” in a democratic election.
Just before you said:
Well just show any simple example where both of those can be true at the same time. What sort of election are we talking about here?
Actually the technical answer is it cannot be done, since Ai was imagining not changing the output. My D and E swap I think gets at what is “weird” about the dictator, and that might be confusing Tel.
Wow, that Arrow’s Impossibility Theorem discussion is really interesting. I hadn’t come across that before. I have a couple of points to add here that haven’t been mentioned:
(1) This theorem only applies to a voting system where the voters must provide a rank order of all the voting options from most preferred to least preferred. This does not apply to systems where you vote for a single candidate or where you give each candidate a numerical grade.
(2) The non-dictator part seems to be a little over-emphasized, both here and everywhere else I’ve seen the theorem discussed. The theorem lays out a set of conditions that would be desirable for a rank-order voting system. Then the theorem proves that it is impossible to satisfy all of those conditions at once with any possible rank-order voting system. One of these conditions is that you cannot appoint a dictator because, ironically, appointing a dictator would satisfy all of the other conditions.
Go through the proof on Wikipedia in detail and you see that the “dictator” must be identified as the pivotal voter (see “Part one: There is a “pivotal” voter for B over A”) and in order for this to happen you need a strict ordering of the voters. I’ll quote from Wikipedia again (same section) : “Now arrange all the voters in some arbitrary but fixed order, and for each i let profile i be the same as profile 0, but move B to the top of the ballots for voters 1 through i.”
The secret ballot process detaches voters from ballots and thus prevents any “fixed order” being imposed on the voters. This is not an accident, it’s a very specific design of the voting process which must collect accurate information regarding the counts but simultaneously must destroy information regarding the identity of the voters.
I disagree with that as well, here’s the second criteria from Wikipedia:
This criteria outlaws the use of a coin toss or other random device to work as a tie breaker (the results in some cases would change due to the coin toss even when no voter changes ballot, therefore outlawed by the criteria). Actually using a coin toss is quite a common method and IMHO a perfectly reasonable thing to do if you have a small group of people and find yourselves often running into tied outcomes (e.g. the Steve Landesberg example of pizza toppings).
Also, in most real-world electoral processes there is only one winner and no second prize so the whole obsession with accurately ranking the losers in the election seems really strange, even if you do require the voters to supply rank order on the ballots.
For example, the Australian lower-house elections require each voter to fill in rank order (which happens to use numbers by convention, those numbers are ordinal not cardinal) but the published results only show first preference counts for each candidate plus the winning candidate after preferences are distributed. There’s no output rank order provided… nobody is freaked out by this, they just don’t care because only the winner gets a seat in Parliament. You might be interested in the margin, or in how many people vote for various issue-based parties to get a feel for the electorate, you can make your own decision based on first preference counts.
Yes the dictator is the pivotal voter. Whether you actually hold an election or not, the dictator always gets his way. That is how dictatorship works. We’re trying to come up with a consistent way to combine many rank-order ballots into a single group preference list. One method that would be consistent but undesirable would be to pick one person as a dictator and always use that person’s ballot as the output ballot. For the purposes of Arrow’s Impossibility Theorem, this solution is not acceptable.
You said:
Forget about ties. Even if you added the exception, “Ties may be broken by a coin toss,” to the set of conditions, the theorem would still hold.
You said:
…says the guy who’s obsessed with tie breakers and secret hidden dictators 😉
But seriously, it isn’t about ranking the losers. It is about finding the correct winner. You can’t take a collection of rank-order ballots and combine them in a way where you can say, “This candidate would have won a head-to-head matchup against every other candidate on the ballot.” You can come up with a non-dictator way of combining the ballots, but it will necessarily fail at least one of the other conditions of Arrow’s Impossibility Theorem.
You’ve been asking for an example: Let’s say you and I have come up with a system for combining rank-order ballots into a group preference order. In our system, there is no dictator. We decide to hold 2 test runs with the same set of voters to see how well our system works. In the first test run, candidate X wins. In the second test run, candidate X does not win and is ranked below candidate Y. Neither test requires a tie-breaker. During these tests, we tracked all of the voters’ ballots and were able to determine that no voter changed his ordering of X and Y relative to one another on his ballot from one run to the next.
Now Tel, do you think that this test has revealed a flaw in our system?
The electoral system in USA and UK are pretty hopeless for ranking preferences of candidates. It may be OK for producing the least worst option for most people. Nobody votes for third party candidates in the USA because they have no hope of success. I think the number of votes they get is way less than the number of people that prefer them. A couple of times recently more people voted for the candidate that ultimately lost. In the UK 4 million people voted for UKIP and they got 1 MP. For labour it only took about 25,000 votes for each MP. People are daft if they don’t vote tactically because otherwise their vote will be “wasted”. Although there is a strong case that their vote is wasted anyway. The systems we have do not produce a dictator, but neither do they produce a result representative if preferences, so it fails anyway.
My take-away from Arrow is that whatever system you have tere will be some inconsistency, so there is no point seeking perfection. You have to pick the inconsistencies that you dislike the least. So PR has one set of problems, but first past the post has another set and neither can be shown to be the only obvious choice of system.
What’s really weird in all of this is that I did NOT say in Tom’s podcast, “Arrow showed a fair social choice function leads to a dictator.” Rather I said that Arrow showed no social choice mechanism can satisfy some obvious criteria, such as non-dictatorship and unanimity. So even on your guys’ own terms (Tel and Craw), your objections to me are misplaced. You are railing against other people’s attempts to popularize the theorem.
This might be my favorite comment thread on the whole internet. It gives this one featured in this video a run for its money:
https://www.youtube.com/watch?v=eECjjLNAOd4
That link is hilarious I never saw that before.
There are odd things possible with the dictator which make an Arrow dictator different from a Stalin dictator.
one is that he cannot order anything he wants. There was a specified set of conditions x1….x n. The dictator only has fiat over those. If “build a concentration camp” is not one of the listed values for x then dictator might not be able to impose it.
It might not be possible to tell who the dictator is until after the election. If the social choice is a list drawn at random from those submitted this will be the case. In this case the dictator actually might not be known, if the drawing was anonymous and multiple voters submitted the drawn list. There is a dictator, we just don’t know who it is.
So Tel is right that dictator is used a bit oddly. (He is wrong on pretty much everything else here.)
No, this is the thing Tel is wrong about most of all, and unfortunately so are you. I agree that if the word “dictator” was being used to denote someone whose individual preference list matched the social preference list in one particular case, that would not match the common-sense usage of dictator. And Arrow’s theorem would not very impressive. But in actual fact, Arrow’s theorem’s says use of the word dictator exactly matches the common-sense usage.
I suggest you look very carefully at Wikipedia’s formal statement of the theorem. The non-dictatorship condition states “There is no individual, i whose strict preferences always prevail. That is, there is no i ∈ {1, …, N} such that for all (R_1, …, R_N) ∈ L(A)^N, a ranked strictly higher than b by R_i implies a ranked strictly higher than b by F(R1, R2, …, RN), for all a and b.” en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem#Formal_statement_of_the_theorem
Understand what that means. R_1 is the preference list of the first person, R_2 is the preference list of the second person, etc. So you have a set of N preference lists, one for each of the N people. So a given set of N preference lists corresponds to what you call one planet. So now look at the condition again. It does not say, “For each planet, there is no individual i whose preference list R_i matches the social preference list in that planet.” It says “There is no SINGLE i such that in ALL planets, that individual’s preference list always matche the social preference list.” So it exactly matches the common-sense meaning of dictator.
And in a dictatorship, you can always identify who the dictator is, even without knowing what the dictator’s preferences are or what anyone else’ says preferences are. If you need to know the details of different people’s preferences to know whose preference list the social preference list will match, then it’s NOT a dictatorship.
The thing is that the dictator criteria will apply IF you stick to the other criteria. By sticking to the other criteria it turns out that one person always gets what they want. What happens in practice is you don’t stick to the other criteria, so you don’t get a dictator.
You left out the “domain of the constitution.” But that is key.
The definition of dictator in Arrow is simple: his preferences become the social preferences over the set of alternatives. That is all.
Look again at my simple of a complete set of preferences over a finite domain above in response to Murphy. The set rule Clinton … Craw IS a valid social choice in that case and IS non dictatorial.
So are my random draw examples.
I mean IS dictatorial. There is a person whose choice becomes the social choice. Tel in the first case, Kirk in the second.
Craw, you are simply wrong. The social rule “Clinton Trump Nader Craw always wins” is simply not a dictatorship. It’s not enough for the social preference list to match Tel’s preference list in one case and Kirk’s preference list in another case. The social preference lists has to match the same person’s preference list in all cases. Only a social rule of the form “Tel’s preference list always wins” or “Kirk’s preference list always wins” is a dictatorship.
If the condition said “for each (R_1, …, R_N) ∈ L(A)^N, a ranked strictly higher than b by R_i implies a ranked strictly higher than b by F(R1, R2, …, RN), for all a and b” then yes the social rule “Clinton Trump Nader Craw always wins” would violate that condition.
But that’s not what the non-dictatorship condition says. It says “there is no i ∈ {1, …, N} such that for all (R_1, …, R_N) ∈ L(A)^N, a ranked strictly higher than b by R_i implies a ranked strictly higher than b by F(R1, R2, …, RN), for all a and b.” The social rule “Clinton Trump Nader Craw always wins” does not violate that condition, so it’s not a dictatorship.
Understand the crucial difference between these two statements. It’s key to understanding Arrow’s theorem. (And if you think that you already understand the difference between these two statements, please explain the difference.)
Let me fix an important typo. The second paragraph should say “If the condition said “for each (R_1, …, R_N) ∈ L(A)^N, there is no i such that a ranked strictly higher than b by R_i implies a ranked strictly higher than b by F(R1, R2, …, RN), for all a and b” then yes the social rule “Clinton Trump Nader Craw always wins” would violate that condition.”
Keshav, this is like what, the 8th time you’ve posted that definition using formal notation? I don’t think it does anything. If you didn’t already know what the theorem was saying, seeing that notation out of context is not really helpful.
Craw wrote: “The dictator only has fiat over those. If “build a concentration camp” is not one of the listed values for x then dictator might not be able to impose it.
It might not be possible to tell who the dictator is until after the election.”
No, Craw, this is totally wrong. Email Landsburg and ask him if you don’t trust me.
It is not long over a year ago that emailing Arrow himself was ruled out as a possibility.
Another way to look at it, paraphrasing Landsburg’s example of the Pizza choices, wjhich I think is correct.
The set-up is three people, three toppings. On one particular day each topping is voted once first, once second and once third. The result is a tie. Whatever system you use to separate the toppings they come out equal
Unless you appoint one person for that day and adopt their preference, or simply adopt one of the choices (which must match one person’s preference)
That sounds fine, but if you adopt the other Arrow criteria, then that person’s preference will forever be selected, for all choices of those three toppings. Landsburg’s post explains why.
That person is described as the dictator. This does not mean that they can decide to build a gulag. (Nor can they decide that there are 8 days in a week, or that 3.5 workouts per week is a meaningless concept).
Craw,
After re-reading this whole thread, I better understand what’s going on. I think you and Tel are getting tripped up with the proof techniques of the theorem, versus the actual statement of the theorem.
Also, I apologize I misunderstood what you were saying about the concentration camp stuff. (I thought you were saying, “The dictator is only able to exercise control in a few scenarios where the other preferences go a certain way.”) But yes, if you’re saying, “Landsburg’s pizza dictator doesn’t have the power to tax your income, just to pick toppings,” then yes that’s right.
This thread, translated to number theory:
BOB: All integers > 1 have a unique prime factorization.
TEL: Ha! How about Pi? Does that have a unique prime factorization?
KESHAV: Well, no but we are talking about integers…
TEL: So, now you’re telling me that Pi is an integer?!
BOB: No, Pi is NOT an integer.
TEL: Right, so the theorem doesn’t apply just to integers! And what’s more, it’s stupid!