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Warren, Re: [EM] DH3 pathology, margins, and
winning votes
--- In [EMAIL PROTECTED],
Chris Benham <[EMAIL PROTECTED]> wrote:
> > Warren, > I have two main points in reply to your "DH3 pathology" anti-Condorcet > argument. > > > DH3 scenario with strategic votes by the A- and B-voters. #voters > > Their Vote > > 37 C>A,B>D > > 32 A>D>B,C > > 31 B>D>A,C > > > > Then the pairwise tallies are going to be: > > > > Definitely A,B > D > C > > Probably C > A,B > > > > In which case we (probably) have a Condorcet cycle scenario. (It is > > actually two 3-cycles which share the common DC arc.) The weakest > > defeats in these cycles are C>A,B which means, under both every > > Condorcet rule I know of (since I think they all are equivalent in the > > 3-cycle case) and Borda, that one of {A,B} is going to be the winner. > > > > I verified that A wins in the 50-50 mixture case under Tideman ranked > > pairs <RankedPairs.html>, Schulze beatpaths <SchulzeComplic.html>, and > > basic Condorcet by using Eric Gorr's Condorcet calculator > > <http://www.ericgorr.net/condorcet/> using this input > > > >37:C>A>B>D > >37:C>B>A>D > >32:A>D>B>C > >32:A>D>C>B > >31:B>D>A>C > >31:B>D>C>A > The first is that those "defeat-dropper" style algorithms (like > Beatpath, Ranked Pairs, River,MinMax) that as you say are all equivalent > in the 3-cycle case > are not my favourites. I prefer both DMC ('Definite Majority Choice', > which allows voters to enter approval cutoffs) and Schwartz,IRV (which > elects the > member of Schwartz set highest ordered by IRV on the original ballots). --Can you go thru how those two new methods would work? CB: Certainly. Schwartz,IRV: "Identify the members of the Schwartz set, but drop no candidates from the ballots. Commence a normal IRV count. When all but one Schwartz set member x has been eliminated, elect x". For this method I favour allowing truncation, but not above bottom equal-ranking. It is much better than Schwartz//IRV, which drops non-Schwartz set members from the ballots before applying IRV. Of course Smith verus Schwartz isn't a big deal. Definite Majority Choice. "Voters submit ranked ballots with approval cutoffs. Truncation and equal-ranking allowed. Ballots with no approval cutoff specified are interpreted as approving all candidates ranked above bottom or equal-bottom. Eliminate all candidates that are pairwise beaten by a more approved candidate. Among the remaining candidates, one (x) will pairwise beat all the others. Elect x." http://wiki.electorama.com/wiki/DMC Several other algorithms are equivalent. Also quite good in my opinion is the simple version with no approval cutoffs which just interprets all ranked (above equal-bottom) candidates as approved . My current favourite method that uses high-intensity range ballots is this "automated version": "Inferring ranking from ratings, eliminate all non-members of the Schwartz set. Then interpret the ballots as approving those candidates that they rate (among those remaining) above average (and half-approving those they rate exactly average). Based on these thus derived approvals, and again inferring ranking from ratings, apply DMC." > My second point is that in your scenario the A and B supporters seem > mainly concerned to elect their favourites, so in that case why wouldn't > they simply be guided in their strategy by their favourite candidates? Seeing how > they stand in the polls, it would be in the interests of both A and B to > make a preference-swap deal at the expense of C. That way they each increase > their chances of being elected form below 33% to about 50% without anyone > having to flirt with the car-crash. --That sounds like naive bunk. The problem with that is, how the hell do voters "make a deal" with each other? This whole "deal" idea is a myth. It is unenforcable and votes are secret ballot and nobody can make a deal with a gazillion voters anyhow even if it were enforceable and verifiable. CB: "Naive bunk"? It is regular practice in Australian elections for seats in Parliament. Admittedly this is helped a lot in most jurisdictions by truncation not being allowed. The candidates are normally obliged to register "tickets" with the electoral commission in advance of the election, partly so attempts to manipulate the result by distributing bogus "how-to-vote" cards can be detected and stamped on. Unless there is automatic and/or long standing cooperation based on ideological affinity the parties/candidates negotiate preference deals with each other. Party volunteers on election day hand out how-to-vote cards to voters on their way in to vote. Most voters take at least one and follow one of them. In your example, based on the sincere preferences, the candidates seem to be about equidistant from each other on the "political spectrum". With a clear front-runner (C) and the other two (A and B) too close to call, the A and B candidates both gain a lot from swapping preferences. If the voters are so concerned to elect their favourite as to be prepared, on their individual inititiative, to recklessly gamble with D, then I think enough of them would be happy to instead just follow their favourite's how-to-vote card to prevent D from being elected. Heck, if that were your view, why not have them all make a deal to vote honestlyIt is certainly possible for all the respectable viable candidates to agree to put some pariah candidate bottom on their tickests. That has happened in Australia. Chris Benham |
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