Re: [EM] Forced strictly-dishonest strategy is common in Schulze-beatpaths voting
Warren Smith writes:
I will sketch a proof that, in Schulze beatpaths voting in random
N-candidate V-voter elections (V--infinity, N fixed):
with probability a positive constant C (where C goes to 1 as
N--infinity):
at least a constant fraction K of the voters (where K goes to 3/4
as N--infinity)
will regard it as strategically forced that they order DE for at
least one
candidate-pair {D,E} for which they honestly prefer ED. By
forced I mean,
they'll feel if they don't do this, they'll have lower expected utility.
Can you follow up with a proof sketch of the fraction of debaters who
have no ethical compunctions about inventing a scenario and then
arguing that they can prove how a supermajority of a population will
*feel* about that invented scenario?
Beyond the obvious inefficiency, one reason that current electoral
systems are loath to repeat elections (even in substantially similar
form, such as runoffs) is that repetition permits a variety of
strategic considerations between iterations, including focused
violence or intimidation. Outlining the extent to which this is true
in random elections with arbitrarily large numbers of both
candidates and voters is not particularly informative.
As the number of candidates increases without bound, the distance
from any given point to the candidates, or between candidates, tends
to decrease -- much in the same way that distance between points
converges to unity in high-dimensional space. Given that Condorcet
methods are susceptible to order reversal, that is exactly the kind of
scenario where you would expect it to be more likely to have an
effect, but the per-voter benefit averaged over random elections
goes down as the number of candidates goes up.
So accepting, arguendo, that 75% of voters might -- a posteriori --
gain expected utility from strategic order reversal, to conclude how
they would feel about that requires an argument that they care more
about the vanishingly small gain in utility than they do about honesty
in voting.
Michael Poole
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why the concept of sincere votes in Range is flawed.
Jonathan Lundell writes: On Nov 25, 2008, at 8:45 PM, Kevin Venzke wrote: --- En date de : Mar 25.11.08, Abd ul-Rahman Lomax [EMAIL PROTECTED] a écrit : What Approval sincerely represents from a voter is a *decision* as to where to place an Approval cutoff. But is it not true that what *all* methods sincerely represent from a voter are the decisions related to voting under that method? If a decision makes sense in a given context, then that is a sincere decision. Is that not your stance? It shouldn't be. Sincere is a term of art in this context, not a value judgement. An insincere vote is simply one that does not represent the preference of the voter if the voter were a dictator. There's nothing *wrong* with voting insincerely (or, equivalently, strategically), in this sense; a voter has a right to do their best to achieve an optimum result in a particular context. Sincere is fine as a term of art. The limitation with sincerity under that definition is that it only applies to the top N choices in an N-winner election. Most strategies involve manipulation of lower rankings. Abd's post made the error of conflating insincere voting with strategic voting, and the further error of claiming that neither approval nor range systems are ever vulnerable to strategic voting -- rather than restricting the hypothesis to sincere votes. Michael Poole Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why the concept of sincere votes in Range is flawed.
Abd ul-Rahman Lomax writes: And now that rarity from me, an original post Approval Voting is a special case of Range, with rating values restricted to 0 and 1. When Brams proposed Approval, it was as a method free of vulnerability to tactical or strategic voting, i.e., voting with reversed preference in order to produce a better outcome. And, indeed, both Range and Approval are immune to that, i.e., there is no advantage to be gained by it, ever (at least not in terms of outcome). The proponents of other methods attacked this by redefining -- without ever being explicit about it -- the meaning of strategic voting. Because the concept was developed to apply to methods using a preference list, whether explicit on the ballot or presumed to exist in the mind of the voter, a strategic vote was one which reversed preference, simple. But with Approval and Range, it is possible to vote equal preference. Is that insincere if the voter has a preference? The critics of Range and Approval have claimed so, and thus they can claim that Range and Approval are vulnerable to strategic voting. Your definition is wrong. A strategic vote is one that is not representative of the voter's honest views or ideal outcome. When using strictly ranked systems (where no ties are allowed), the only possible form of insincerity is order reversal. When using approval and range voting, preferences may be insincerely magnified or diluted, in addition to being reversed. As a thought experiment, consider the case where I would score three candidates as 100, 50 and 0 on a uniform scale. If I know that the first two candidates are close in the polls, I may vote for them as 100, 10 and 0 so that my preferred candidate's chance of winning is increased. This is a strategic vote in the usual sense. You attempt to redefine strategy so that it is not called one. Rambling about ideal abstractions, inevitable voter knowledge, and so forth does not change that it is a distortion of my honest ratings based on desired outcome and beliefs about other ballots. Strategic voting works *only* in the case of (believed) knowledge about how a significant number of other voters vote. If you delude yourself into thinking otherwise, and on that basis convince yourself that range voting does not suffer from -- or even permit -- strategic voting, you will only undermine your own credibility. Michael Poole Election-Methods mailing list - see http://electorama.com/em for list info
