[EM] 3 or more choices - Condorcet

[Juho Laatu]

On 11.11.2012, at 18.33, Chris Benham wrote:

> Kevin Venzke wrote:
> 
> "Margins, it seems to me, is DOA as a proposal due to the Plurality criterion.
> That 35 A>B, 25 B, 40 C would elect A is too counter-intuitive."
> 
> I agree. For those who don't know, the Plurality criterion says that if  X is ranked
> strictly above all other candidates on more ballots than Y is ranked above any candidates,
> then Y must not win. 

Woodall says:  (in http://www.votingmatters.org.uk/ISSUE6/P4.HTM)
If some candidate x has strictly fewer votes in total than some other candidate y has first-preference votes, then x should not have greater probability than y of being elected.

Wikipedia says:
If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of winning must be no less than B's.

Plurality criterion assumes implicit approval ("given any preference") of ranked candidates (definitions above have some differences). In that sense it adds something extra to pure ranking.

If one wants to have an approval cutoff in the ballot, an alternative approach is to have an explicit approval cutoff. Explicit cutoff allows voters to rank also candidates that they do not approve. Those explicit approvals would be taken into account when counting the results (maybe in the spirit of the Plurality criterion). Implicit cutoff (if voters know of its existence) may encourage truncation, which means losing some preference information.

Typically the definitions of winning votes based Condorcet methods do not contain any reference to implicit approval, and usually they don't have any specific emphasis on the last and one but last position. But of course, if they meet Plurality criterion, then they will respect rankings or rankings above the last position as described in the Plurality criterion.

In the given example there was an assumption (in the spirit of the Plurality criterion) that all voters who voted K>L, did not approve M and N, and they all approved L. That may not be the case if voters are not aware that this is how their vote will be interpreted, or they may not follow this rule even if they knew it.

I wonder if the voters should be told about the Plurality criterion or if that should be hidden from them (to avoid them rankig only those candidates that they approve / want to promote). In some startegies that information may be useful to them. But losing information because of truncation (in an election that has no meaningful strategy problems) is harmful.

Juho



> 
> http://wiki.electorama.com/wiki/Plurality_criterion
> I like a more general standard that says that if  X both pairwise beats Y and positionally
> dominates Y, then Y mustn't win.
> 
> Chris Benham
> ----
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