[EM] Losing Votes (equal-ranking whole)

[Kristofer Munsterhjelm]

On 01/06/2019 14.15, Faran, James wrote:
> 51 A>B>C>D
> 49 B>C>D>A
> 
> Is A a better choice than B?
> 
> 1. Yes. Plurality demands it. Moreover, B beats C and D on all ballots,
> so C and D can be ignored and the pairwise race is all that's left.
> 
> 2. No. A is ranked bottom on 49% of ballots, B ranked at least second on
> 100%, top on almost half.
> 
> Are C and D Irrelevant Alternatives?

Oh, I see. This is a seeming paradox, because it seems like B should win
as A is all the way at the bottom on the 49 votes.

However, the counterintuitive bit is that we can't infer strength of
preference from how many candidates are in play. That's what Borda got
wrong. E.g. there's no difference between

51: A>B>C>D
49: B>C>D>A

and

51: A>B>C>D>E>F>G>H>I>J>K>L>M
49: B>C>D>E>F>G>H>I>J>K>L>M>A

or

51: A>B>C
49: B>C>A

as far as the suitability of A (or B) is concerned.

Another note: it's not just Plurality that demands it. The majority
criterion demands it.

Now I'm wondering if there are cloneproof rules that, like Borda, prefer
everybody's second choice even if it means breaking the majority
criterion. In one sense, yes: Range counts if you relax what
"cloneproof" means. In another, no: only ranked rules can be subject to
strict (ranked) clone independence, and in any of these that don't meet
majority, a majority acting in concert can masquerade as many
non-majority blocs and thus alter who the winner is.