[EM] Maximal Lotteries

[Daniel Kirslis]

I have always seen the participation criterion defined as 'Adding votes
that rank candidate A over B will not make it more likely for candidate B
to win over candidate A'. The proof that Markus shared appears to establish
that any Condorcet method will fail this criterion. It is not dependent on
how the lotteries are defined over the Smith set, because it hinges on the
fact that when a Condorcet winner exists, their probability of winning is
100%. It constructs an election with a cyclic tie between 4 candidates.
Then, it shows that the tie can be broken to create a Condorcet winner by
adding votes that rank that Condorcet winner second, thus moving those
votes' first place candidate from a non-zero probability of winning to a
zero probability of winning.

On Wed, Jun 25, 2025 at 12:57 PM Closed Limelike Curves via
Election-Methods <election-methods at lists.electorama.com> wrote:

> Markus—different generalizations/definitions of no-show (equivalent in the
> deterministic case) yield different results in when you allow lotteries.
> I'd have to double-check which is satisfied for Maximal Lotteries, but the
> most common are either:
> 1. Turning out to vote will always yield a better lottery than not turning
> out, or
> 2. Turning out to vote will probably improve the outcome for you, i.e. if
> you do a random draw from the winning lottery if you do vs. don't turn out
> to vote, you will prefer the random draw from the one where you turn out
> more often than vice-versa.
>
> On Tue, Jun 24, 2025 at 5:27 AM Markus Schulze via Election-Methods <
> election-methods at lists.electorama.com> wrote:
>
>> Hallo,
>>
>> it has been proven by Moulin that the Condorcet
>> criterion and the participation criterion are
>> incompatible:
>>
>>     Herve Moulin, "Condorcet's principle implies
>>     the no show paradox", Journal of Economic Theory,
>>     volume 45, number 1, pages 53-64, 1988,
>>     DOI: 10.1016/0022-0531(88)90253-0
>>
>> Here is a short version of Moulin's proof:
>>
>>
>> http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011042.html
>>
>> Markus Schulze
>>
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>>
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>
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