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

[Juho Laatu]

On 11.1.2014, at 14.39, Michael Ossipoff <email9648742 at gmail.com> wrote:

> These might be the same definitions that i posted a few years ago, probably some time roughly around the beginning of 2011. Or maybe the earlier ones are different and better. But, for now at least, the following is what i mean by "Voting X over Y":
>  
> This first one is what I mean. I like it best. The 2nd one is only for if there is a voting system to which the first one doesn't apply, if there's a voting system that won't return a result with just 1 voter:
>  
> 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.
>  
> [end of 1-voter definition of voting X over Y]
>  
> That's what I mean by "voting X over Y"

The intention on this definition seems to be very close to my intentions when I used term "effective ranking". This definition clearly covers also those candidates that the voter did not mention in the ballot (I wanted to be clear that the idea was to talk about the actual effect of the vote, not just about what the voter wrote on the ballot).

If I try to look possible remaining small differences, 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). The same could apply also in scenarios where the voter can give both (linear) rankings and approvals if they are independent of each others.

>  
> 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]

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).

Juho


>  
> Michael Ossipoff 
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