On 05/10/2012 08:55 PM, Michael Ossipoff wrote:
I emphasize that I don't know if u/a FBC makes a satisfactory guarantee.
I imagine it would be like the independence of clones criterion. Properly speaking, independence of clones only take into account exact clone candidates. It would be easy to contrive a method that removes clones as a first pass and would pass the letter of clone independence. However, such a method is very fragile and the protection is not real, whereas in real methods, the protection extends beyond exact clones. Similarly, I'd imagine a method that passes u/a FBC but not regular FBC to be almost completely protected when all but one voter votes u/a style, a little less with two voters, a little less with three, and so on.
With it, FBC must be complied with only if the election is u/a to everyone. So, someone wanting to write a failure-example would have to devise an example in which, for everyone, there are 2 sets of candidates such that hir preferences within the sets are negligibly weak in comparison to hir preference between the sets. And there must not be anything that positively rules out a win in the less-preferred set. I don't know if satisfying that criterion would guarantee that there couldn't be societally-damaging favorite-burial incentive. I don't know for sure if I could write a really precisely-worded u/a FBC, because I haven't previously written criteria that refer to preference-strength, or in which the premise contains a stipulation that a win in a certain set not be positively ruled out.
I think you can make it votes-only. Say the initial statement of the criterion is something like:
Assume every voter divides the candidates into acceptables and unacceptables, and also has a true preference ordering where all acceptables are ranked above all unacceptables. Then there must not exist a voter that can only switch the win from one of his unacceptables to one of his acceptables by voting someone else than his favorite first.
The division and the true preference ordering is hidden information. But you might "infer" it from the votes by taking a worst-case approach, something like: There must not exist a voter, that were his internal division between candidates to put X among the acceptables and Y among the unacceptables, and were his internal preference order to have Z as his favorite, the only way he can switch the win from Y to X is to vote someone else than Z top.
Or, simplified: There must not exist a voter for which there exist two different candidates {X, Z} along with the current winner Y, so that the only way he can switch the win from Y to X is to vote someone else than Z top on a ballot that ranks X above Y.
Is that just regular old FBC?
And I don't know if Smith-Top would pass that criterion. But, as I said, the matter is of interest, because I consider FBC to be important, because of the societal consequences of failing it. If a weaker FBC such as u/a FBC could be sufficient, then more methods would be acceptable. Anyway, Smith-Top means what you'd expect it to mean: Elect the Smith set member who is ranked in 1st place on the most ballots.
I'm less sure that would pass u/a FBC. It might be the case that you have a large Smith set and would have to vote Compromise above Favorite so Worst doesn't win the tiebreaker, whereas in Approval, you always support the two equally.
Smith-Top obviously meets Condorcet's Criterion. Smith-Top would be a method in the spirit of Kristofer's Smith-Approval, but attempting to copy ICT's defection-resistance. Smith-Top is to Smith-Approval as ICT is to ICA. I'm not proposing Smith-Top, for the reasons given above. Kristofer: Let me know if you intended u/a FBC different from how I've described it. Mike Ossipoff ---- Election-Methods mailing list - see http://electorama.com/em for list info
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