Hi,
On Apr 4, 2005, at 20:21, Jobst Heitzig wrote:
We know of course that most often
one can easily find two measures which do not agree on which candidate
is "best", so we're left with deciding which measure is most important.
But what if no measure is "most" important but each is important in some
sense or other? Then perhaps there is a most important sense in which
measures can be important... etc...
When we are talking about sincere criteria we could as well leave the decision to the community that arranges the election. It is possible that different elections are aimed at electing different kind of winners. Sometimes the winner maybe should be the one with least enemies, sometimes one that is accepted by as many as possible etc. There can thus be many different sincere voting methods. This means that "best candidate" (and social ordering) is relative to the criteria that the community has set for this election.
in the unlikely case in which the winner becomes unavailable between the election and the time of taking office, one would rather hold a new election than put the "2nd best" candidate in office...
Few observations on this topic:
Yes, there is no need for a single winner method to be able to say who was second best. If this ordering is available, it could be possible in some cases to reuse the results of the first election if the winner becomes unavailable. Many voting methods indicate the result as numerical values, in which case it is easy to see what the ordering is. The new winner however need not be the second best candidate.
Minmax is one such method. It uses only orderings in the ballot. If the winner becomes unavailable one could expect the orderings to stay the same even if one of the candidates had not participated in the election. (Maybe some people would have ranked more candidates if one of their favourites was missing but let's ignore that.) Although the rankings would be the same with the remaining candidates, the result should be calculated again since it seems natural that one should now compare each candidate only against the other remaining candidates, i.e. not against the unavailable old winner. For this reason the second best (first minmax round) candidate maybe would not be the new winner. But we would be able to calculate the winner pretty reliably without arranging new elections.
In the example above we had actually two alternative orderings. Maybe both can be used, but for different use. (If the used voting method was minmax (margins), then the ordering showed how many additional votes each candidate would have needed in order to become a Condorcet winner, in the case where the first winner (a) is a candidate or (b) is not.)
In some multi winner elections like parliamentary elections the ability to reuse the ballots is maybe more useful. It is quite probable that some MPs must be replaced between two elections. Some voting methods might however recommend to make bigger changes than just elect one new candidate to replace the lost one. => Some problems..
So, I suggest we should drop the idea of "social ordering" altogether
Word "altogether" is a bit strong for me, but surely social preferences are more complex than just one ordering.
Best Regards, Juho
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