robert bristow-johnson wrote:
what do you mean: "weight"? rankings are just rankings. if a voter
ranks Candidate A above Candidate B (independent of what the absolute
rank values are), all that means is that this voter would vote for A if
it were a simple two-candidate race with B. and all Condorcet seeks to
accomplish is to be consistent with that social choice regardless if
Candidate C or Candidate D were in the race or not.
it's pretty simple:
1. if a majority of voters agree that Candidate A is a better choice for
office than Candidate B, then Candidate B is not elected. this imposes
consistency with the 2-candidate race where we all agree who should be
elected and why.
2. the relative merit of Candidate A to Candidate B is not affected by
the presence of a third candidate, C. in the converse, this means that
removing any loser from the race and the ballot, that this should not
change who the winner is. if it does, that loser is a "spoiler". it is
precisely the motivation for adopting IRV in the first place.
To my knowledge, Condorcet passes IIA whenever there is a Condorcet
winner. If Condorcet winners are frequent, that's a pretty good property.
That is, if candidate A is a Condorcet winner, and you remove some other
candidate B, A is still the Condorcet winner. If you add some other
candidate C, unless C beats A, A is also still the Condorcet winner.
Some may not like the tradeoffs Condorcet bring (like failing FBC), but
it bears keeping in mind, I think. While IIA (general
spoiler-independence, as it were) might be too strong to be sensible in
the general case, having a method pass it in certain cases is welcome.
Advanced methods can go further, as well: a method that passes
independence of Smith-dominated alternatives will not be influenced by
candidates outside the Smith set.
(Of course, if there's rarely a CW or if the Smith set is usually large,
this doesn't amount to much. Offensive strategy attempts to create
cycles in the strategists' favor.)
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