[EM] Maximal Lotteries

[Toby Pereira]

 OK, thanks. But being "objectively correct" in the way you describe doesn't necessarily mean it should be our preferred Condorcet method, as I discussed here: https://groups.google.com/g/electionscience/c/wT1_hN38b8s/m/H-ZXeCqFAAAJ
"The point being that if we shift our viewpoint, we are not necessarily looking for the "ultimate in Condorcetness" even if we want a method that passes the Condorcet criterion. It's just one criterion that we want our method to pass, along with monotonicity but not at the expense of everything else. Wanting a monotonic method doesn't mean we just look for the "ultimate in monotonicity" at the expense of everything else."

Toby

    On Tuesday 24 June 2025 at 16:49:35 BST, Closed Limelike Curves <closed.limelike.curves at gmail.com> wrote:  
 
 Maximizes the minimal expected margin of victory in a competition against any other lottery. Essentially extends minimax by allowing for breaking ties using randomness.

The important thing is there is always a lottery that has, on average, majority support when compared to any other lottery.
100% agree this is the "objectively correct" generalization of Condorcet to races with cycles, to the extent that such a thing is possible.
On Tue, Jun 24, 2025 at 8:39 AM Toby Pereira via Election-Methods <election-methods at lists.electorama.com> wrote:

 What is maximal about the lotteries?
Toby
    On Tuesday 24 June 2025 at 13:16:27 BST, Daniel Kirslis via Election-Methods <election-methods at lists.electorama.com> wrote:  
 
 Here you go bud: https://en.wikipedia.org/wiki/Condorcet_winner_criterionhttp://en.wikipedia.org/wiki/Maximal_lotteries
On Mon, Jun 23, 2025 at 8:24 PM Chris Benham via Election-Methods <election-methods at lists.electorama.com> wrote:

I don't know what the "maximal lotteries method" is, and I guess that is 
true of other members of this list. But just going by its name I doubt 
that it would appeal to me.

Is the Condorcet "winner principle" something different from the 
Condorcet criterion?   Because that is a binary pass-or-fail thing.

Chris Benham


On 24/06/2025 7:44 am, Daniel Kirslis via Election-Methods wrote:
> For those of you who believe in the Condorcet winner criterion, is 
> there anyone who doesn't agree that the maximal lotteries method is 
> the theoretically soundest Condorcet method?
>
> Amongst the Condorcet methods, it seems to me that maximal lotteries 
> is clearly the best, at least in principle (that is to say, if we 
> ignore more practical concerns about ease of administration and 
> popular understanding). All deterministic Condorcet methods fail the 
> participation criterion. Therefore, a non-deterministic method is the 
> way to go, and the question becomes: "How shall we assign 
> probabilities amongst the Smith set?" I cannot imagine a more elegant 
> and fair-minded way of doing so than the maximal lotteries method.
>
> Is there anyone out there who understands the maximal lotteries method 
> but still thinks that there exists another method that better 
> satisfies the Condorcet winner principle? If so, why?
>
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