I thought of a simpler way to explain my "safety" fix. The full system description follows, with my new phrasing in bold.
N days before the election, all candidates (including declared write-in candidates) rank order all other candidates (including declared write-in candidates). These orderings are announced. In the election, all voters submit an approval ballot, with two spaces for write-ins. Total approvals and number of bullet votes are counted for each candidate and announced. (Bullet votes are votes for only one candidate, including all valid or invalid write-in votes.) Then each candidate may grant the number of bullet votes they received to N other candidates from the top of their preference list, where N can be any number including 0. All candidates decide what number N to use simultaneously, and then those decisions are announced publicly. *Take the two candidates with the highest approvals. Recount those two as if they hadn't approved each other (that is, without adding any bullet votes from one to the other).* The winner is the candidate *of those two* with the highest approval in this final count. The purpose of removing the mutual votes from the top two before deciding the pairwise winner of these two is, as I explained before, to make it so that one candidate will never lose because they approved another one. This frees candidates to be honest in their approvals. I believe that this system, as described, is pareto-dominant over plurality, asset, and approval. It is also very Condorcet-compliant. That is, assuming that X% of all candidates' voters agree with their candidate's preference order, and that the other (100-X)% have preferences which cancel each other out (random noise); that this X is the same for all candidates; that all voters who do not agree with their candidate do not bullet-vote (voting for a random number of extra candidates), and all voters who do agree with their candidate do bullet vote; and that there is a true pairwise champion; then the pairwise champion will win in a (unique) strong Nash equilibrium. This is a very solid result, which relies on the perfect information of the candidates when choosing how to "delegate" their approvals; it is NOT true of systems such as Approval or even DYN (without the preference-ordering and top-two-pairwise-recount aspects). It is not even true of any Condorcet system I know of (because of strategy)! So this system (and some obvious variants) is in fact *the most Condorcet-compliant* system I know of. Since it is also relatively simple to understand - not as simple as approval, but not too far behind - I think it makes an excellent candidate for a practical proposal. Jameson Quinn > I'd add my "safety" fix to the near-clone problem, *if* someone can think > of an easy way to describe and motivate it. Basically, it looks at any > candidate who mutually approve with the winner, and sees if they would beat > the winner (pairwise) with those mutual approvals turned off. This helps > when, for instance (honest preferences): > > 35: X1>X2 > 25: X2>X1 > 21: Y>>X2 > 19: Y>>X1 > > If X1 and X2 approve each other, the right thing happens (X1 wins), no > matter what Y voters do. If they do not, this fix does not attempt to read > anyone's minds (or to ask people again in a runoff). > >
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