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

[Michael Ossipoff]

>
>
> > 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"
>

You wrote:



>
> 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).


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.


> The same could apply also in scenarios where the voter can give both
> (linear) rankings and approvals if they are independent of each other.
>

I don't know what an example of that would look like, bit it wouid probably
likewise be ok.


>
> >
> > 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).
>

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.

That substitution probably could, and maybe should, be made.

Michael Ossipoff








>
>
> >
> > Michael Ossipoff
> > ----
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