On Aug 21, 2011, at 5:06 PM, Warren Smith wrote: > Kenneth Arrow has worried that range-voting-type "score" votes might have no > or > unclear-to-Arrow "meaning." In contrast, he considers rank-ordering-style > votes to have a clear meaning. > Nic Tideman has also expressed similar worries in email, but now about > the "lack of meaning" of an approval-style vote. > In contrast, I think Tideman regards a plurality-style "name one > candidate then shut up" > vote as having a clear meaning. > > E.g. "what does a score of 6.5 mean, as opposed to a score of 6.1, on > some ballot?" > > But the Bayesian view is: whether or not Arrow or Tideman or somebody > has a more-or-less muddled mental notion of the "meaning" of a ballot, > is irrelevant. The only genuinely meaningful thing is "who won the > election?" > All meaning of any ballot therefore derives purely from the rules > for mathematically obtaining the election-winner from the ballots.
Arrow would not, I think, quarrel with the claim that a cardinal ballot has a pragmatic/operational "meaning" as a function of its use in determining a winner. But but it's an unwarranted leap from that claim to use the ballot scores as a measure of utility. Arrows objection to cardinal scores, or one of them, is that they are not and cannot be commensurable across voters. > > For a simple example of how ballots have no inherent meaning without > voting system rules, consider plurality and AntiPlurality voting in which > the meanings of a "name one candidate" ballot are pretty much opposite > (plurality: most-named candidate wins; > AntiPlurality: least-named candidate wins). > > Let us now enquire more deeply about ballot "meaning." In a non-monotone > voting > system like Instant Runoff, your vote A>B>C can cause A to lose, whereas > your vote B>C>A would have caused A to win. Would Arrow be right if > he said IRV is wonderful > because "A>B>C" has a "clear meaning"? Or would a Bayesian be right > in saying this > example indicates the "meaning" Arrow had in mind, was not valid? Indeed the > Gibbard-Satterthwaite theorem > http://rangevoting.org/GibbSat.html > shows that in essentially ANY rank-order ballot system and also in the > plurality and > AntiPlurality systems with "name one candidate" ballots -- i.e. exactly > the systems Arrow & Tideman thinks "have meaning" -- there ALWAYS > exist elections > in which some voter's vote of A>B>C will cause a worse election winner > (for the A>B>C > notion of "better" and "worse") than some different > dishonestly-ordered vote would > have caused. (And with Plurality and AntiPlurality, "dishonestly" ranking > your non-favorite candidate top or your really-not-worst candidate > bottom, can be the only way > for you to get an improved election result.) > In such an election, what is the "clear meaning" of an A>B>C rank-order vote? > > Gibbard identified/invented exactly two rank-order ballot systems in > which honest and strategic > voting were the same thing (this required him to employ > non-determinism), but stated > that both of his systems were not good enough for practical use since they > "leave too much to chance." > > In contrast, consider the "double range voting" system invented by > F.Simmons and Warren D. Smith > http://rangevoting.org/PuzzRevealU2.html > > This system (or others of the Simmons class) ARE good enough for > practical use if any > rank-order system is (since it leaves only an arbitrarily small amount > of the deciding to chance, > and deviates from your favorite system in an arbitrarily small way). > > In this voting system, each ballot contains a part on which the voter > is urged to > provide her honest scores (on, say, an 0-to-9 range) for each > candidate. In this system, > ONLY voting on this ballot portion in a unique honest manner is strategically > best. Any deviation from perfect honesty (or omision of information) > is a strictly worse voting strategy. > That is, if your expected utility if A wins is 6.5 and your > expected utility for B > winning is 6.1 on an 0-to-9 scale (defining the utility scale so > you've rated the > best available candidate 9 and the worst 0) > then you MUST score A=6.5 and B=6.1 EXACTLY, otherwise you are guaranteed > to get in expectation a worse-utility election result. > > So contrary to assertions by the likes of Arrow that utility is "unmeasurable" > or that range votes "lack meaning" it seems to me that we have a very > clear, totally unique, > not changeable by one iota, meaning for the scores 6.5 and 6.1 deriving > wholy from the procedure the voting system uses to determine the > winner from the votes. > This is wholy unlike EVERY allegedly-practical rank-order voting system. > > So Arrow, and Tideman (and anybody else) are simply wrong if they > assert scoring-style votes > are inherently less-meaningful than rank-ordering-style or > name-one-candiate-style votes. > > So now Arrow might perhaps riposte that to HIM, deep in the recesses > of his brain, > rank-order votes have more meaning, even though every voting system he > and his colleagues have ever considered for practical > use, disagrees with his private meaning in at least some situations, > and even though (therefore) > the true meaning of your vote really also depends on how the OTHER > voters are voting, not just > on the candidates and your evaluation of them in your private brain. > (I would have to then counter-riposte: who cares?) > > Another riposte might be that under the assumption there are a large number > of other voters all of whom vote TOTALLY RANDOMLY and independently, > your vote can have a clear meaning, and in some rank-order systems (e.g. > Borda) > this meaning coincides with "honest ordering." > I would then riposte that (a) that assumption is false, and (b) under > the same assumption > approval voting also has a "clear meaning" (namely: you should > "approve" candidates > above mean utility for you). > > Does our argument tell us that score-style votes inherently have MORE meaning > than rank-order style votes? (Exactly contrary to Arrow?!?) Well... not > necessarily. Yes, score-style votes certainly inherently convey more > information > than rank-ordering-style votes (strengths of preference as well as > preferences). > And I would claim that if they were employed for the honest-part of > double range voting > ballots, they inherently have more meaning. But if employed for plain > range voting, then it is posible > to construct 4-candidate election situations in which it is strategically best > for a range voter to misorder, so we run into the same > Gibbard-Satterthwaite-style issues (albeit only with 4, not 3, candidates). > > All this analysis really tells us is the Bayesian view is correct. > And certainly that any dismissal > of range- or approval-style voting on the grounds of their claimed > "inherent lack of meaning", > is hogwash. > > -- > Warren D. Smith > http://RangeVoting.org <-- add your endorsement (by clicking > "endorse" as 1st step) > ---- > Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
