SMITH's REPLIES TO ATTEMPTS TO CRITICIZE RANGE VOTING by Warren D Smith Sept 2004 I promised to reply to all the main criticisms of my Range Voting paper (http://math.temple.edu/~wds/homepage/works.html #56) that appeared on ApprovalVoting@yahoogroups.com as soon they "died down to a dull roar." So here we go. CRITICISM 1. Some object to my explicit or perceived morality-based attacks (?) on "dishonest" strategic voters. REPLY: Sorry to carelessly cause that misimpression; I did not intend to make moral arguments, only scientific ones. I usually employ the terms "honest" and "rational" voter mainly since 1 letter shorter than "sincere" and "strategic"... I will say, however, that on average the net effect on society of many strategic voters acting in their own greedy interests, usually is negative compared to the hypothetical situation where all those voters were honestly portraying their interests. An excellent example of this dichotomy is the fact that Nebraska and I think Maine (and under consideration: Colorado) donate their electoral votes to the president proportionally, whereas all other states distort the picture by giving them ALL to the plurality winner. I.e. Nebraska has chosen to be honest, not strategic, and the price they paid is that they've disenfranchised themselves and made sure no president will ever pay any attention to them. So being honest instead of strategic is bad for Nebraska. But it is good for the country - the country as a whole would be better off if every state were to adopt Nebraska's honesty policy. In fact, federal laws should force them to. CRITICISM 2a. Fisher had the idea that range voters obviously will be strategic since nobody would be stupid enough to be honest. Hence, it will just be approval voting anyway. Hence there is no need for range, stay with approval. 2b: But others had the opposite idea that those poor dumb voters in their teeming masses, although they want to be strategic, will be too dumb to know how under range voting, thus giving a large relative advantage to the few smart voters who recognize how to be strategic. This was supposed to be a criticism of range voting but not of approval voting. REPLY: Well, of course 2a & 2b contradict one another. (Maybe you should fight it out.) But anyway, I'll shoot 'em both down. Anti-2a: I claim that a substantial number of voters will choose to be honest and not strategic. In Bush-Kerry 2004, about 4% will vote 3rd party. This is very unstrategic. So at least 4% of voters are honest. I in fact think it is more like 10-30%, but it might be as high as 70%. (About 33% of voters register as 3rd or independent even though it is strategically better to say Repub or Democ. So in this decision we have at least 33% honesty.) In fact what really is astonishing is that, despite making this argument, Fisher HIMSELF is one of those honest voters who apparently does not understand how to be strategic/dishonest!! Observe: Fisher says he is voting Badnarik. Strategically stupid, but honest. Fisher has the idea he will do this "vote buddy" thing where he finds somebody who would have voted Kerry, pairs off with him, and both buddies agree to not vote Repub & Democ respectively, but 3rd party instead. Strategic? Well, no. The actual best strategic play for some Kerry-supporter to SAY they would have voted Democ, and agree to be a vote buddy with some would be Bush-supporter like Fisher - and in fact not just with one such Fisher, but in fact with 572 Fishers. All the 572 Fishers then dutifully deny their votes to Bush. Result: our Kerry supporter has, by being strategic, got 573 votes worth of extra support for Kerry vs Bush. Because the US has secret ballots and it is illegal to sign a contract to vote X, this strategy by the Kerry supporter is wholy legal. And as I said, we are not going to discuss morals. I am only going to say that Fisher, if he is being honest with us, is clearly acting in a nonstrategic/honest manner in the voting booth, despite his idea that only "gullible fools" would ever do so. We learn several things from this. First, suppose Fisher and his vote buddy really were somehow mentally connected via a mind bridge so that they could not be dishonest=strategic with one another and acted as a single super-organism. In that case, this vote buddy behavior WOULD be rational, even though for single independent organisms it isn't. This is another example of the fact that greedy rational behavior for SINGLE people can be non-best for COLLECTIONS (in this case 2) of people. Which is also how it can be that it would be best for society as a whole, if everybody were honest, not strategic, in their vote! Second, the urge to express oneself honestly is a powerful human drive, as we've seen so powerful as to cause strange irrational behavior even in one so normally coldly rational as Fisher. Indeed, it is irrational for essentially every voter to vote. [If your chance of affecting the election is 1 in a billion (say) and it costs you $1 to vote (in transport, wasted time, etc) then it is irrational to vote unless the election result is worth more than $1billion to you.] Thus the only reason almost all people vote AT ALL is due to this powerful irrational drive. That is how powerful it is. Given this observed property of human beings, and given the fact that having lots of honest voters is better for society, WHY WOULD ANYBODY POSSIBLY WANT APPROVAL VOTING INSTEAD OF RANGE? Range permits people to express their true opinions; approval voting forces them not to and denies their powerful basic human drives which would have helped society as a whole, if only they had been permitted to emply range voting. (Incidentally, if I may speculate a bit: why is it that many humans have this irrational drive to be honest? I suggest to you it is a consequence of Darwinian evolution - societies with more more-honest and fewer more-strategic&dishonest people, were "fitter" and survived, while other societies collapsed causing their inhabitants to die out more often. I suggest encouraging the former kind of society by adopting RV and not AV.) Third: if you really want to be strategic, then a range voter can do so and essentially act like an approval voter. Thus, from the standpoint of strategic voters, the situation with RV is exactly the same as with AV and there is not one iota of disadvantage for RV. Indeed in their view there is an ADVANTAGE, namely some other woters may foolishly be honest, giving the strategic voter a little more relative power. So strategic voters should prefer RV over AV. And honest voters should also prefer RV over AV, since it obviously permits them to be a hell of a lot more honest. Anti-the rest: Well, your view is cockeyed. You've become so steeped in pro-AV thinking that you've actually deluded yourself into believing that it is good to have more people vote strategically and non-honestly. Nonsense. Furthermore, if you really believe range voting strategy is so hard people will be too dumb to figure it out, then consider the fact they'll have experts from the parties and on TV telling them for years how they should vote maximally strategically in the upcoming election... Some of my critics also subscribe to the fallacy that there will be different voter interest-groups, some of whom will consist of honest voters and others of strategic voters, and the latter will under range voting kill the former, whereas under approval voting both sides would have acted strategic and the stronger side would (rightly) win. In principle it is correct that an interest group of strat voters will beat an interest group of honest voters, and this is true in ANY voting system, not just range voting. But... are there such groups? Anywhere? Ever? If my critics could cite historical examples where some side in some big voting battle consisted of poor little honest voters who just never thought of strategy because they were just too morally good, whereas the other side consisted of smart nasty voters who were strategic in their votes and therefore evilly won, then I might take them seriously. The truth is, every large interest group will consist of some percentage of honest & strategic voters and will have advisors telling their constituencies how they'd prefer them (strategically) to vote, and will have voters who listen to and do not listen to that advice. The critic's picture of the world here, is just not a valid picture of the world. Still... this criticism has some validity. As examples, consider Bush-Gore 2000, where the poor little honest liberal Gore voters sometimes voted Nader and hence lost the election to the Evil Bush. Does this mean democrats are just morally better and more honest in their votes and hence are doomed? Well no: in Nixon-Humphrey 1968, the repubs nearly lost because of many among them who voted for the ultraconservative George Wallace, and in fact Nixon *did* lose to Kennedy 1960 arguably because of the effect of the conservative 3rd party candidacies (Byrd+Barry Goldwater/Strom Thurmond and the National State's rights party). So in both R and D parties, there are some honest voters who vote nonstrategically and can cause damage to their causes... under AV, and also under RV, Gore 2000 and Nixon 1968 would both have won. In general, though, more voter honesty on average (though not always) results, under RV, in better society-wide utility, and more benefit comes thusly than under AV - and that is the experimental bottom line. Finally, if you believe that in approval voting, everybody will know how to vote strategically, or wrongly believe best strategy in AV is the same as honesty, then consider the following example. if the pre-election polls say A,B,C,D are successively less likely to win (and these are a spherically symmetric gaussian...) and your honest opinions are A=0.30 B=0.50 C=1.00 D=0.55 then in a large election your strategically best approval vote will be A=0 B=1 C=1 D=0 contradicting your honest belief D>B. CRITICISM 3. Recall: I had stated that a clear case where RV was superior to AV was the 2002 CA governor election with 135 candidates listed in random order. No voter could know about most candidates. Most voters only know about, say, 5 of them. In that state of ignorance, under AV, most voters would "play it safe" by disapproving of the other 130. But really they should regard the unknowns as "about average" and hence give them some "about average" score intermediate between 1 and 0. (Perhaps one would still wish to play it safe by not awarding, say, 0.5, but rather, 0.4.) Thus Range Voting here avoids a tremendous and harmful bias caused by approval voting. AV here FORCES voters to have a HUGE bias. Range voting permits them to pick a more reasonable bias, or none at all. That permits those other voters who DO know about a candidate to have a much better chance of having their knowledge not be wasted. The criticism of this: in AV, any voter has the option of rolling a specially weighted dice to randomly award the unknowns 1 or 0 with expected score 0.4 (or whatever). So (the critic continues) RV does not really have this advantage over AV. REPLY: Well, this criticism is valid in principle. But in practice, hardly any voters are going to go to the trouble to get specially biased dice and, inside the voting booth, to roll them all 130 times and then push or not push 135 buttons. Hence in practice, the election will be essentially unaffected by voters adopting this method. Hence it wlll instead be hugely biased by voters adopting the easier method of "just say no". Hence in practice, my argument for RV over AV WAS fully valid. (Further, this dice suggestion, even if it ludicrously happened, would introduce undesired statistical noise in AV. So again RV would have an advantage over AV.) Finally, I claim that mathematically, honest approval voting is a pretty bad election method in situations with a single winner and an enormous number of candidates. It essentially results in a pretty random selection from among the top half (here it would have been the top 67) of the candidates. Experiments show far better behavior in that limit for Borda, Black, and range PROVIDED the voters are honest. In this kind of situation, it really pays for society to have a system permitting honest voters to have their say. It is pretty much they, and they alone, who get to provide distinguishability among the top 67. So in range voting with 90% strategic voters and 10% honest ones we would here have something like a 67-way tie as far as the strategic voters were concerned, which would be broken by the 10% honest ones allowing the best candidate to often win. (This in a situation where, say the top 67 all are better than the bottom 68 and all know it, but there is also a clear gradation within the top 67.) I've oversimplified, but you see my point: just small % of honest voters in RV can have a huge helpful-to-society effect in situations like this, while AV would leave those honest voters very frustrated with their inability to express themselves and the result would be bigtime bad for society: 30X-worse winner!) CRITICISM 4: My range voting paper had at one point claimed Merrill's previous computer study must have had a bug because he found 100% "social utility efficiency" in 2-candidate elections. My critic claimed I'd misunderstood Merrill and actually he was ok. RESPONSE: At first I thought my critic was right. He sounded right and it would have fit in very neatly with a number of things... But I have now re-examined Merrill (both his book and also his paper A comparison of Efficiency of Multicandidate Electoral Systems, Amer J Polit Sci 28 (1984) 23-48) and sorry, I still think Merrill and my critic were wrong. Merrill's "SUE" is really the same thing as my "Bayesian regret" except he scales it so that elect-random-winner has SUE=0 and hypothetical-best-candidate has SUE=100%. (Bayesian regret of hyp-best-canddt is 0 and of random-winner is whatever it is, so you can readily convert. I prefer to give the raw regret numbers instead of this cleaned up version because some scenarios have larger rand-winner regrets than others and SUE hides that truth.) I also re-read Bordley: Amer Polit Sci Rev 77 (1983) 123-141 who computed utilities following my policy. It is not true Merrill's utilities were normalized so the best candidate in the eyes of any particular voter had util=1 and the worst 0. In Merrill's "random society" they are random values in [0,1] but NOT strategically altered so max=1 min=0. (I understand why you got that impression but my reading of Merrill says it aint so.) Therefore, Merrill had a *bug* because SUE should NOT have been 100% for everything with 2 candidates. (Or, no bug and Merrill just lied when telling us what he did. Either way, bad.) Merrill found approval was best in 3-canddt elections and Borda was best if >=4 candidates. However, this was with honest voters. If Merrill had tried strategic voters Borda would have looked a lot worse and approval would still be top for 3,4,5 candidates. And honest range voting is superior to honest approval voting, which Merrill would have found had he ever tried range voting. CRITICISM 5: There is something wrong with Smith's whole reliance on measurements of "Bayesian regret." The critics had various ideas about what the wrongness might be: 5a: Smith suffers from the "averaging fallacy" that if (when choosing between alternative A and B) two voters think A is better by 49 utility units, but one voter thinks B is better by 100, then it would be better for society to choose B. 5b: Smith has artificially contrived his definition of Bayesian regret and utilities so that the honest-voter-range-winner is the SAME as the optimal winner, thus assuring that range voting comes out looking "best" in the later comparative measurements. Quote by my critic: "the optimal candidate is the one elected by a range vote with 100% sincere, omniscient voters... Forgive my brutal frankness, but did you [Smith] really need a simulation to discover that under that metric, range voting was optimal?" 5c: Smith has the wrong definition of Bayesian regret; regret = the expected value of SUM_{all voters v} utility[O][v] - SUM_(all voters v) utility[C][v] = the expected value of SUM_(all voters v) (utility[O][v] - utility[C][v]) where C is the actual winner and O the optimal hypothetical winner (maximizing the first sum). Some critics suggest instead that "a more useful metric would be SUM_(all voters v) (utility[O][v] - utility[C][v])^2, i.e. least squares or perhaps MEDIAN_(all voters v) utility[O][v] - MEDIAN_(all voters v) utility[C][v]." REPLIES: anti-5a: It is no fallacy: B is truly better. In fact, this scenario is equivalent to the following: if A gets elected, you are beheaded and your worldly wealth distributed to the two other voters. combined anti-5a and anti-5c: The reason Smith is right here is a definition: "utility" is not exactly the same thing as money (although in my earlier email I had carelessly implied it was). It is roughly translateable to dollars units, but is not exactly the same as dollars. It is more like "happiness". More precisely still, utility is BY DEFINITION the thing that we truly want society to maximize the sum of. Now regret is then truly measuring the extent to which some election method, (in expectation in a random election scenario) falls short of maximizing utility. So it is what we truly want society to minimize by choosing the right voting system, because we will then maximize average societal utility over a long sequence of elections in the future. The critic's alternate ideas in 5c are bad, especially his first. We do not want a "metric" (measuring a "distance"); we want a measure of overall societal happiness, and we want our voting system to maximize it, and we want to measure the extent by which that has falied to happen. The least squares idea would not do that, and in fact it would heavily penalize a candidate leading to nearly as much happiness as did O, but by very different methods: If O made all democrats (51%) happy and all repubs (49% of society) sad, but C made all repubs happy and all dems sad, then C would induce nearly as much happiness as O, but by your very bad least squares measure would be an extremely "bad" choice, in fact "worse" than a candidate who made everybody sad! The critic's median-based idea is better but really only maximizes the happiness of ONE, supposedly "median" individual, instead of maximizing the sum of everybody's happiness. Probably correlated to the right thing, but not the right thing. anti-5b: This would be a great criticism if it were true, but it is false. The claim by my critic: "the optimal candidate is the one elected by a range vote with 100% sincere, omniscient voters..." is false. The truth: The optimal would be elected by a NONrange vote (a summation of true utilities, but with no bounds on the range) with 100% sincere, omniscient voters. There were two very important differences here: (1) the elimination of upper and lower bounds on the range, and (2) in my experiments with "honest" range voters the voters did not report their utilities, but rather rescaled and translated them so the best candidate in their eyes had util=1 and the worst 0, THEN reported them. My critic continued on, but then was criticizing something I never said. Anyhow, consequently, range voting, even with 100% honest voters, has nonzero regret, even in 2-candidate elections. CONCLUSION: The bottom line is that range voting ALWAYS had SMALLER OR EQUAL regret, in experiments, than EVERY other voting system tried (including IRV, condorcet, Borda, approval, and plurality) in EVERY experimental scenario tried, and with either honest, or strategic, and/or partially ignorant, voters. These measurements are not contrived, and Bayesian regret is the uniquely right thing to measure, and it is roughly translateable into very real terms such as dollars or wasted lives. And that is why both I, and Merrill, and Bordley, and Weber, all invented it (I'm not sure how many of these 4 were independent, but I suspect 3). Finally, the utility-difference by which range > plurality, is experimentally greater than the amount by which plurality > random-candidate-wins. Probably monarchs were on average somewhat better than random-winners (trained from birth to rule...) so the range-plurality difference exceeds the plurality-monarch difference by EVEN MORE. That tells us that switching to range voting would be a larger improvement in "democracy" than the entire invention of democracy. The stakes are that high. There has rarely been any occasion in history when there has been an opportunity to get so vast an improvement for so little cost.