[EM] Detailed stats for the ordinal methods

[Chris Benham]

>
> Strategic nomination can indeed be a problem and should be 
> investigated more closely. James-Green Armytage showed that IRV has 
> greater exit incentive than the Condorcet-IRV methods do, for instance.

Kristofer,

Can you please point me to this?

Chris

On 12/05/2024 6:18 am, Kristofer Munsterhjelm wrote:
> On 2024-05-09 23:56, Closed Limelike Curves wrote:
>> Hi Kristofer! Thanks for this :)
>>
>> I do want to ask though, do you think the rate of manipulable 
>> elections is a good measure of the "general strategy resistance" of 
>> an electoral method? The resistant set certainly seems to reduce that 
>> rate, but for all I know that 7.5% is all turkey-elections.
>
> The narrow sense of turkey elections - exploiting nonmonotonicity to 
> do pushover - must, for ordinal methods, belong to the "Other" 
> strategy category. Not every Other strategy need to be pushover, but 
> pushover must be an Other strategy. Let's consider Resistant,Borda again:
>
>>>          Ties: 0.001 (5)
>>>          Of the non-ties:
>>>
>>>          Burial, no compromise:        123     0.0246246
>>>          Compromise, no burial:        72      0.0144144
>>>          Burial and compromise:        147     0.0294294
>>>          Two-sided:                    48      0.00960961
>>>          Other coalition strats:       1       0.0002002
>>>          ================================================
>>>          Manipulable elections:        391     0.0782783
>
> There's only one out of 4995 elections with "other" strats. So 
> pushover manipulability is very low. (I've designed resistant set 
> methods that seem to have no pushover at all, even though they fail 
> monotonicity. I haven't been able to prove why certain resistant set 
> constructions make pushover impossible, though.)
>
> I can think of two ways to formalize the broader category of 
> turkey-raising as mentioned on Electowiki. They would be:
>     - Supporters of candidate A encourage a candidate C to enter, so 
> that C>B>A voters express their honest opinion; but that makes A win 
> instead.
>     - By making C appear to have more support than he actually does, 
> supporters of candidate A trick strategic B>C>A voters to compromise 
> for C. As a result, the winner changes from B to A.
>
> Neither effect is captured in my simulations: the first would be a 
> form of strategic nomination, and the second is a strategic play under 
> imperfect information. As the number of candidates doesn't change, and 
> the simulation involves a fully honest election followed by 
> full-information strategy, it doesn't capture either.
>
> Strategic nomination can indeed be a problem and should be 
> investigated more closely. James-Green Armytage showed that IRV has 
> greater exit incentive than the Condorcet-IRV methods do, for 
> instance. I haven't written code to do this, and thus my stats don't 
> provide any information about strategic nomination.
>
> Taking the second effect into account would be very difficult, as 
> we're then moving into a repeated game of imperfect information. But, 
> as a heuristic, if the voters know that the method has low (ordinary) 
> manipulability, then it would probably be harder to get them to engage 
> in a self-destructive strategy as well, since it would be harder to 
> get them to engage in strategy in general.
>
> And a final caveat: if you combine a strategy resistant method with 
> primaries or other parts, the composition could have turkey 
> strategies. I imagine that the likelihood of this happening depends on 
> the strategic nomination incentives for the method: so you could see 
> it with IRV but it would be less likely with Smith-IRV.
>
> -km
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