[EM] Random Ballot fails IIAC

[Markus Schulze]

Dear Mike,

you wrote (19 Jan 2002):
> Say the voting system is Random Ballot.
>
> Say there are just 2 candidates, and all the voters vote for their
> favorite. Now we add a 3rd candidate.
>
> Say, in this big national election with 100,000,000 voters, there's
> one voter who doesn't watch the news or read newspapers or magazines,
> and hasn't read the materials at the polling place. He's heard
> something about a new voting system, but he doesn't know that it's
> a completely new voting system as opposed to Plurality with a more
> reliable count procedure. Or, if he does, he doesn't know that it's
> so profoundly different that Plurality strategy no longer applies.
>
> Say that new candidate is that voter's last choice. He feels strongly
> that his 2nd choice has a much better chance of beating that new last
> choice, and so, being a lesser-of-2-evils voter, he now votes for
> his 2nd choice instead of his favorite. His 2nd choice, one of the
> 2 original candidates, now gets one more vote than he'd get if the
> new candidate hadn't been added. The addition of the new candidate
> has increased a previously-existing candidate's probability of winning.
>
> This is why I asked Markus if anything was stipulated about how people
> vote. He indicated that there's no such assumption. For that reason,
> Random Ballot fails IIAC, as Markus defined it.

Of course, when you presume that criteria should be defined on the
sincere opinions of the voters and that the voters don't vote sincerely,
then there is also no method that meets Condorcet, Pareto, monotonicity,
participation, consistency or clone-independence.

Markus Schulze