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<div dir="ltr" data-setdir="false">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.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">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.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Thanks</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Toby</div><div><br></div>
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On Monday, 6 April 2026 at 04:50:45 BST, Joshua Boehme via Election-Methods <election-methods@lists.electorama.com> wrote:
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<div><div dir="ltr"><br></div><div dir="ltr">Here's what I get:<br></div><div dir="ltr"><br></div><div dir="ltr">#1: 7/15 A, 5/15 B, 3/15 D<br></div><div dir="ltr">#2: D<br></div><div dir="ltr">#3: B<br></div><div dir="ltr">#4: A<br></div><div dir="ltr">#5: 5/13 A, 7/13 B, 1/13 C<br></div><div dir="ltr">#6: C<br></div><div dir="ltr">#7: B<br></div><div dir="ltr"><br></div><div dir="ltr"><br></div><div dir="ltr">The following are cases where adding votes with candidate X at the top of <br></div><div dir="ltr">the ballot causes X to go from a positive probability of winning to a zero <br></div><div dir="ltr">probability:<br></div><div dir="ltr"><br></div><div dir="ltr">#1 -> #2<br></div><div dir="ltr">#1 -> #4<br></div><div dir="ltr">#5 -> #6<br></div><div dir="ltr">#5 -> #7<br></div><div dir="ltr"><br></div><div dir="ltr">The general pattern here is that a lottery over the additional voters' <br></div><div dir="ltr">first, second, and third choices switches to a definitive win by their <br></div><div dir="ltr">second choice. Without knowing the underlying utilities of the voters, <br></div><div dir="ltr">whether or not they prefer that resulting outcome is impossible to <br></div><div dir="ltr">determine. [1]<br></div><div dir="ltr"><br></div><div dir="ltr"><br></div><div dir="ltr">[1] Once you go down that rabbit hole, it gets harder to stand by Condorcet <br></div><div dir="ltr">/ Smith as a strict requirement. Indeed, it's easy to construct examples of <br></div><div dir="ltr">elections -- not necessarily in these particular cases -- where *every <br></div><div dir="ltr">voter* prefers, say, a random ballot lottery to a Condorcet winner<br></div><div dir="ltr"><br></div><div dir="ltr"><br></div><div dir="ltr">On 4/5/26 6:20 PM, Kevin Venzke via Election-Methods wrote:<br></div><div dir="ltr">> Hi Toby,<br></div><div dir="ltr">> <br></div><div dir="ltr">> I think it must not be the same criterion.<br></div><div dir="ltr">> <br></div><div dir="ltr">> It doesn't seem like Moulin's incompatibility proof assumes determinism.<br></div><div dir="ltr">> <br></div><div dir="ltr">> I see on the Talk page Markus has helpfully linked it, or his interpretation of it:<br></div><div dir="ltr">> <a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011042.html" rel="nofollow" target="_blank">http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011042.html</a><br></div><div dir="ltr">> <br></div><div dir="ltr">> I don't know how to compute the Maximal Lotteries method to try the proof, though.<br></div><div dir="ltr">> <br></div><div dir="ltr">> Kevin<br></div><div dir="ltr">> votingmethods.net<br></div><div dir="ltr">> <br></div><div dir="ltr">> <br></div><div dir="ltr">> <br></div><div dir="ltr">> Le dimanche 5 avril 2026 à 08:29:27 UTC−5, Toby Pereira <<a href="mailto:tdp201b@yahoo.co.uk" rel="nofollow" target="_blank">tdp201b@yahoo.co.uk</a>> a écrit :<br></div><div dir="ltr">>> <br></div><div dir="ltr">>> My understanding was that Maximal Lotteries (a non-deterministic Condorcet method) did pass participation. <a href="https://en.wikipedia.org/wiki/Maximal_lotteries" rel="nofollow" target="_blank">https://en.wikipedia.org/wiki/Maximal_lotteries</a><br></div><div dir="ltr">>> <br></div><div dir="ltr">>> Toby<br></div><div dir="ltr">>> <br></div><div dir="ltr">>> On Saturday, 4 April 2026 at 01:16:10 BST, Kevin Venzke via Election-Methods <<a href="mailto:election-methods@lists.electorama.com" rel="nofollow" target="_blank">election-methods@lists.electorama.com</a>> wrote:<br></div><div dir="ltr">>>> <br></div><div dir="ltr">>>> <br></div><div dir="ltr">>>> Definitely not. Very few methods satisfy Participation, certainly not ones that<br></div><div dir="ltr">>>> resemble Condorcet. The most complicated Participation methods are DAC and DSC.<br></div><div dir="ltr">>>> <br></div><div dir="ltr">>>> <br></div><div dir="ltr">>>> Kevin<br></div><div dir="ltr">>>> votingmethods.net<br></div><div dir="ltr">> ----<br></div><div dir="ltr">> Election-Methods mailing list - see <a href="https://electorama.com/em" rel="nofollow" target="_blank">https://electorama.com/em</a> for list info<br></div><div dir="ltr"><br></div><div dir="ltr">----<br></div><div dir="ltr">Election-Methods mailing list - see <a href="https://electorama.com/em" rel="nofollow" target="_blank">https://electorama.com/em</a> for list info<br></div></div>
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