[EM] So I got an email... / IIA

[Kristofer Munsterhjelm]

On 12.04.2022 20:39, Kevin Venzke wrote:
> Hi Kristofer,
> 
> Le mardi 12 avril 2022, 03:23:18 UTC−5, Kristofer Munsterhjelm <km_elmet at t-online.de> a écrit :
>> Do you (or any EM readers) have a name proposal for these methods? I was
>> thinking possibly "Top Opposition", because it's about some quality of
>> the candidate being evaluated, being compared to some quality of an
>> opposing candidate - a candidate who beats the first one pairwise. But
>> perhaps that's too hard to understand. Any better ones? :-)
> 
> I'm not sure, names like fpA-max(fpC) are more descriptive than we usually get.
> It might be hard to top.
> 
> To me "opposition" usually suggests that it may not be a pairwise win.

Yeah, as a descriptive name, fpA-max(fpC) is pretty good, but it may
seem nonsensical if you don't know the context. I was thinking of a
"friendly name" (like "instant runoff voting").

Forest's seems a little over the top :-) He has a point, though, that
some of the friendly names sound like "super duper majority everywhere
voting". It's a difficult balance to get right.

>> As for the methods themselves (sum and max): according to Kevin's
>> simulations, they're pretty similar. Mine has a lesser compromising
>> incentive, his has a lesser burial incentive.
> 
> I think the Plurality criterion difference is noteworthy. With "max," at least
> one candidate will have a positive score, and any candidate disqualified by
> Plurality will have a negative score.
> 
> Plurality isn't a strategy criterion, but at least in the example I sent you
> there was an appearance that the Plurality-disqualified "sum" winner could have
> been using a random fill strategy:
> 
> 0.327: D
> 0.322: B>A>C>D
> 0.186: A
> 0.164: C

That's a good point. I guess I was thinking that extending towards DMTBR
is more novel than getting Plurality resistance, so I'd like to try that
first. But for a public proposal, Plurality is definitely a desirable
criterion.

>> The reason I constructed
>> mine is that (I think?) it's less susceptible to crowding.
>>  
>> E.g. suppose that A wins (B is the candidate with most first prefs who's
>> beating A pairwise), and for C, D is the candidate with most first prefs
>> beating him pairwise. We clone D (so that each clone has fewer first
>> preferences). Then the penalty term to C's score decreases, which could
>> lead C to win. On the other hand, the sum is unaffected because it'll
>> just sum the clones' first preferences up no matter how many there are.
>>  
>> Both are vulnerable to vote-splitting, though, because of the fpA term.
> 
> Yes, you seemingly can't get away from Clone-Winner issues with these.

Here's a concept that popped into my head last night:

Let v be the number of voters, S be a set of candidates, C the set of
all candidates, and C\S be the set of every candidate but the ones in S.
Let f(S) = v if someone in S is the CW, otherwise f(S) is the sum of all
candidates in S's first preferences, minus the first preferences of
every candidate in C\S who beats at least one candidate in S.

Now f(S) stays the same no matter how you clone candidates in C\S. And
if you clone A, f({A}) before the cloning is the same as f({A1, A2})
after the cloning - indeed pre-cloning f({A} union S) is the same as
post-cloning f({A1, A2} union S) for any S.

Perhaps f can be arranged in some way to create clone independence? E.g.
something like DAC/DSC, sorting sets by their f value and intersecting.
I don't know if that would preserve DMTCBR or DMTBR though; it gets very
murky very quickly.

-km