[EM] Adjusted Condorcet Plurality, an interesting new LNHarm+LNHelp method

[Kevin Venzke]

Hi Kristofer,

> On 1/22/23 17:55, Kevin Venzke wrote:
> > Hello,
> > 
> > Here is the procedure for "Adjusted Condorcet Plurality":
> > 
> > 1. From the submitted rankings, identify the first preference winner (FPW).
> > 2. Edit all the ballots so that all preferences below the FPW are removed/truncated.
> > 3. On the revised ballot set, check for a Condorcet winner. Elect them if there is one.
> > 4. Else elect the FPW.
> 
> That's nice and indeed interesting!
> 
> My method finder wouldn't have found this because (if I understand it 
> right) it's not summable.

I have been assuming it isn't summable since at first glance you have to determine the FPW
first, and then in a second pass get a pairwise matrix. But that's it. I'm not sure what
the precise definition of summability is, but could it be allowed to do this in one pass?

If there are n candidates then you need to track n + n( n(n-1) ) figures, counting in one
pass. It's comparable to a single 3D matrix.

My DNA framework technically can find this method, but realistically I wouldn't have found
it this way, because it wouldn't have appeared to be definable in any terms I had thought
of.

> Does your simulator have a strategy susceptibility calculator? If so, is 
> it any good on that measure?

Not an overall susceptibility measure, just a collection of miscellaneous ones, two of
which (truncation and burial) won't show anything for this method.

The performance is very similar to IRV (which should make sense since with three candidates
they are the same method). With four candidates and five blocs:

Condorcet Loser: IRV satisfies, ACP does not
Mono-add-top failures: IRV satisfies, ACP does not
Mono-raise failures: ACP is 23% worse
Condorcet efficiency: ACP .8% better
CDTT efficiency: ACP .7% better
Compromise incentive: ACP 2.6% better
Winner has a majority against them: ACP 3.8% better
Minimal defense failures: ACP 4.3% better
SFC failures: ACP 4.4% better

Maybe I should provide another pairing to show that these numbers are mostly pretty small.
So here's a few numbers but comparing Bucklin and DSC to IRV.

Condorcet efficiency: Bucklin 15% worse (than IRV); DSC 13.5% worse
CDTT efficiency: Bucklin 4.6% better; DSC 7% worse
Compromise incentive: Bucklin 49% better; DSC 7% worse
Winner has a majority against them: Bucklin 19.7% better; DSC 31% worse
Minimal defense failures: Bucklin satisfies this; DSC 67% worse
SFC failures: Bucklin 6.2% better; DSC 41% worse

Not sure if that helps but in short, it seems like ACP might show tiny gains in some areas,
in exchange for worse monotonicity and clone independence, and also Condorcet Loser
failures.

Kevin
votingmethods.net