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

Michael Ossipoff email9648742 at gmail.com
Sat Jan 11 04:39:49 PST 2014

```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"

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]

Michael Ossipoff
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