Maximal Lotteries
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?
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?
Election-Methods mailing list - see https://electorama.com/em for list info
Even when the Condorcet criterion is taken as granted I think also methods that elect outside of the Smith set can be considered best in the sense that they elect the ideal winner with sincere votes.
Juho
On 24. Jun 2025, at 1.14, Daniel Kirslis via Election-Methods election-methods@lists.electorama.com 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?
Election-Methods mailing list - see https://electorama.com/em for list info
Here you go bud:
https://en.wikipedia.org/wiki/Condorcet_winner_criterion
http://en.wikipedia.org/wiki/Maximal_lotteries
On Mon, Jun 23, 2025 at 8:24 PM Chris Benham via Election-Methods <
election-methods@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?
Election-Methods mailing list - see https://electorama.com/em for list
info
Election-Methods mailing list - see https://electorama.com/em for list
info
What is maximal about the lotteries?
Toby
On Tuesday 24 June 2025 at 13:16:27 BST, Daniel Kirslis via Election-Methods election-methods@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@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?
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
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@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@lists.electorama.com wrote:
Here you go bud:
https://en.wikipedia.org/wiki/Condorcet_winner_criterion
http://en.wikipedia.org/wiki/Maximal_lotteries
On Mon, Jun 23, 2025 at 8:24 PM Chris Benham via Election-Methods <
election-methods@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?
Election-Methods mailing list - see https://electorama.com/em for list
info
Election-Methods mailing list - see https://electorama.com/em for list
info
Election-Methods mailing list - see https://electorama.com/em for list
info
Election-Methods mailing list - see https://electorama.com/em for list
info
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@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@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@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@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?
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info