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

[Toby Pereira]

 Some interesting findings, thanks Joshua and Kevin for those. So it seems that given that there are possible utility scores where participation would be failed, Maximal Lotteries can't be said to pass, since passing means in all cases.
It's interesting what you say, Joshua, about Condorcet / Smith as a strict requirement. I've never felt that it's something voting methods must adhere to in all circumstances, but there are still pragmatic reasons for using complying methods in many situations.
Thanks
Toby
    On Monday, 6 April 2026 at 04:50:45 BST, Joshua Boehme via Election-Methods <election-methods at lists.electorama.com> wrote:  
 
 
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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