Investigating criterion compliance
I first started thinking that monotonicity and resistant set might be
compatible due to a program I wrote that would find minimal
manipulability methods for a restricted number of candidates and voters.
This program showed that minimum manipulability was not markedly
affected by insisting on monotonicity, at least for three candidates up
to ten voters, and four candidates with 4-5 voters.
Given this, and that I eventually ended up finding a monotone resistant
set method, I thought I'd next try to create a more general automated
proving program to rule out certain criterion combinations. Such a
program would return either "these criteria definitely can't all be
passed by the same method" or "don't know".
If I do end up writing something like that, what combinations of
criteria would you be most interested in investigating?
-km
Hi Kristofer,
If it's in scope of what you're proposing, I think Mono-add-top + Smith is the biggest outstanding one.
I can't quite picture how your program would tackle this. My DNA framework also essentially gives "definitely not" or "don't know." Unfortunately these two criteria are in the latter category (i.e. they actually look compatible). But the framework offers rather limited maneuvering room to test Mono-add-top.
Another apparent compatibility in my framework is Condorcet and Later-no-help. They're known to be incompatible, but I dumped a lot of time into trying to understand how such a method would work according to the framework. Then I discovered I already had a named method that supposedly meets both. I plan to make a post on this soon, kind of interesting.
Kevin
votingmethods.net
Kristofer Munsterhjelm via Election-Methods election-methods@lists.electorama.com a écrit :
I first started thinking that monotonicity and resistant set might be
compatible due to a program I wrote that would find minimal
manipulability methods for a restricted number of candidates and voters.
This program showed that minimum manipulability was not markedly
affected by insisting on monotonicity, at least for three candidates up
to ten voters, and four candidates with 4-5 voters.
Given this, and that I eventually ended up finding a monotone resistant
set method, I thought I'd next try to create a more general automated
proving program to rule out certain criterion combinations. Such a
program would return either "these criteria definitely can't all be
passed by the same method" or "don't know".
If I do end up writing something like that, what combinations of
criteria would you be most interested in investigating?
-km
On 2025-09-06 00:57, Kevin Venzke wrote:
Hi Kristofer,
If it's in scope of what you're proposing, I think Mono-add-top + Smith is the biggest outstanding one.
I can't quite picture how your program would tackle this. My DNA
framework also essentially gives "definitely not" or "don't know."
Unfortunately these two criteria are in the latter category (i.e.
they actually look compatible). But the framework offers rather
limited maneuvering room to test Mono-add-top.
Mine will be similar to the DNA generator, except with thousands to
millions of scenarios. When it finds something that passes, it should
constructively give the mapping "if in this election, elect these
candidates".
If we're lucky and it says "don't know" about Smith + MAT, then we'd be
left with a lot of concrete outcomes across election space giving a
method that passes both for a low number of voters and candidates. It's
still very difficult to deduce a general method from it, though.
And if I'm ambitious enough, I know there's a way to turn "definitely
not" into a Woodall/Moulin-type disproof, i.e. "definitely not, and this
is why". A paper I read a while back showed how to do that with
participation, but it's still quite a bit of work to get it done! So I
think I'll leave that for later, if I see a particularly interesting
combination that it says is incompatible and I don't understand why.
Another apparent compatibility in my framework is Condorcet and
Later-no-help. They're known to be incompatible, but I dumped a lot of
time into trying to understand how such a method would work according to
the framework. Then I discovered I already had a named method that
supposedly meets both. I plan to make a post on this soon, kind of
interesting.
That's indeed interesting. I thought Woodall had proven them to be
incompatible - perhaps the density of failures is low enough that they
fit all the scenarios in your DNA generator?
-km