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

[Michael Ossipoff]

Juho--

"Vote X over Y" is a generalization of "rank X over Y". In your example,
you're ranking A over B, B over C, and C over A.

You're asking more from the "voting X over Y" defnition than I am. Because
ranking X over Y can (with your hypothetical balloting-system) be done
circularly, there's nothing wrong with voting X over Y to be likewise
circuarly do-able.

You're ranking all 3 candidates over eachother circularly,and you're voting
all 3 candidates over eachother circularly.

You could define someting more global in scope, about your treatment of the
whole set of candidates. But voting X over Y is intended as what you're
doing when you rank X over Y.

Michael Ossipoff.


On Sat, Jan 11, 2014 at 11:02 AM, Juho Laatu <juho4880 at yahoo.co.uk> wrote:

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