[EM] Questions about Majority-Beat vs Plurality-Beat Condorcet

[Joshua Boehme]

Here's what I get:

#1: 7/15 A, 5/15 B, 3/15 D
#2: D
#3: B
#4: A
#5: 5/13 A, 7/13 B, 1/13 C
#6: C
#7: B


The following are cases where adding votes with candidate X at the top of 
the ballot causes X to go from a positive probability of winning to a zero 
probability:

#1 -> #2
#1 -> #4
#5 -> #6
#5 -> #7

The general pattern here is that a lottery over the additional voters' 
first, second, and third choices switches to a definitive win by their 
second choice. Without knowing the underlying utilities of the voters, 
whether or not they prefer that resulting outcome is impossible to 
determine. [1]


[1] Once you go down that rabbit hole, it gets harder to stand by Condorcet 
/ Smith as a strict requirement. Indeed, it's easy to construct examples of 
elections -- not necessarily in these particular cases -- where *every 
voter* prefers, say, a random ballot lottery to a Condorcet winner


On 4/5/26 6:20 PM, Kevin Venzke via Election-Methods wrote:
> Hi Toby,
> 
> I think it must not be the same criterion.
> 
> It doesn't seem like Moulin's incompatibility proof assumes determinism.
> 
> I see on the Talk page Markus has helpfully linked it, or his interpretation of it:
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011042.html
> 
> I don't know how to compute the Maximal Lotteries method to try the proof, though.
> 
> Kevin
> votingmethods.net
> 
> 
> 
> Le dimanche 5 avril 2026 à 08:29:27 UTC−5, Toby Pereira <tdp201b at yahoo.co.uk> a écrit :
>>   
>> My understanding was that Maximal Lotteries (a non-deterministic Condorcet method) did pass participation. https://en.wikipedia.org/wiki/Maximal_lotteries
>>   
>> Toby
>>   
>> On Saturday, 4 April 2026 at 01:16:10 BST, Kevin Venzke via Election-Methods <election-methods at lists.electorama.com> wrote:
>>>   
>>>   
>>> Definitely not. Very few methods satisfy Participation, certainly not ones that
>>> resemble Condorcet. The most complicated Participation methods are DAC and DSC.
>>>   
>>>   
>>> Kevin
>>> votingmethods.net
> ----
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