# [EM] 2 precise and universally-applicable definitions of voting X over Y

Juho Laatu juho4880 at yahoo.co.uk
Sat Jan 11 08:02:29 PST 2014

```On 11.1.2014, at 16.53, Michael Ossipoff <email9648742 at gmail.com> wrote:

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> > One voter definition of voting X over Y:
> >
> > A voter votes X over Y if s/he votes in such a way that, if X and Y were the only candidates, and if s/he were the only voter, and if the voting system is the one in which s/he is voting, then X would be the unique winner.
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> > [end of 1-voter definition of voting X over Y]
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> > That's what I mean by "voting X over Y"
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> You wrote:
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> this definition limits considerations to having two candidates only. In some special situations, like if circular rankings can be used, this definition seems to say that one votes A over B when one votes A>B>C>A (circular).
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> Sure, but that's ok, because, in your circular ranking, you're ranking A over B, even though you're circularly ranking each over the next.

What I mean is that when all three candiates are considered, that circular ranking looks like a tie between those three. All three candidates are in a similar position, and the voter seems to find all three candidates equally good. The election method might not favour A over B based on this vote.

The definition also says that the voter votes A over B, B over C and C over A. Also relationship "voting X over Y" could thus be circular.

I wonder if this was your intention. This might work in your definition DC (?), but I'm not sure if thei is a good general definition of voting X over Y.

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> The same could apply also in scenarios where the voter can give both (linear) rankings and approvals if they are independent of each other.
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> I don't know what an example of that would look like, bit it wouid probably likewise be ok.

The situation is very similar. (I sent one example to you in a private mail. In that example the voter was able to rank the candidates A > B > C > D, and at the same time approve only D and B.)

Juho

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> >
> > But in the event that there's a voting system that won't return a result with just one voter:
> >
> > Many voter definition of voting X over Y:
> >
> > A voter votes X over Y if s/he votes in such a way that, if X and Y were the only candidates, and if the voting system is the one in which s/he is voting, the addition of hir ballot, and 4 other identical ballots, to the ballot-set could change the winner from Y to X, but couldn't change the winner from X to Y.
> >
> > [end of many-voter definition of voting X over Y]
> >
> > That definition assumes that nonmonotonicity can't occur with only two candidates. If it could, then the immediately above-stated definition would have to be replaced by:
> >
> > A voter votes X over Y if s/he votes in such a way that, if X and Y were the only candidates, and if the voting system is the one in which s/he is voting, then the number of configurations of other voters in which the addtition of hir ballot, and 4 identical ones, would change the winner from Y to X, is greater than the number of configuration in which the addition of those ballots would change the winner from X to Y.
> >
> > [end of alternative many-voter definition of voting X over Y]
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> I defined the idea behind effective ranking by referring to increasing the probability of becoming elected. Probabilities could be used also here (maybe easier and more exact).
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> Yes, for that many-voter definition, with the nonmonotonicity-protection (if that's needed), it's briefer to speak of increasing the probability that X will uniquely win, and it probably would work just as well.
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> That substitution probably could, and maybe should, be made.
>
> Michael Ossipoff
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> > Michael Ossipoff
> > ----
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