[EM] A family of easy-to-explain Condorcet methods

[Kristofer Munsterhjelm]

On 6/30/21 11:09 PM, Daniel Carrera wrote:
> -------
> All elections of mayor, city councilors and school commissioners shall 
> be by ballot, using a system of ranked choice voting without a separate 
> runoff election. The chief administrative officer shall implement a 
> ranked choice voting protocol according to these guidelines:
>   (1) The ballot shall give voters the option of ranking candidates in 
> order of preference.
>   (2) A candidate “A” is said to win against another candidate “B” if 
> more voters rank “A” above “B” than rank “B” above “A”. If there is a 
> candidate that wins against every other candidate, that candidate is 
> elected.
>   (3) If no candidate wins against every other candidate, the presiding 
> officer shall remove the candidate with fewest first place votes, in 
> rounds, until one of the remaining candidates wins against every other 
> candidate. That candidate is elected.
>   (4) The city council may adopt additional regulations consistent with 
> this subsection to implement these standards.
> ----- >
> This makes Pb a very realistic proposal for the very real decision next 
> year in Burlington, when the city council will decide whether to adopt 
> some kind of ranked ballot system again.

You probably need to define the list-creating procedure and explicitly 
refer to striking candidates off the list, so as not to confuse the 
method with IRV. I did a cursory check of Reddit and cmb3248 said "IRV 
is literally the same thing [as Pb] except instead of Condorcet winners 
it uses majority winners, something people already get". The 
remove/eliminate distinction seems to be a subtle one that not everybody 
gets.

>>    It's a bit of a tradeoff. Going from Benham to Pb gives you summability
>>    and a somewhat simpler description of the method, but you lose clone
>>    independence.
> 
> 
> Is clone independence a big problem in Pb? This is an intentionally 
> vague question. I'm trying to distinguish between problems that are very 
> likely to happen very often in real elections and theoretical problems 
> that are unlikely to show up often. Split votes in FPTP is by far the 
> world's best known example of electoral failure, whereas my 
> understanding is that Minimax is only affected by clones if you have 
> three clones in a cycle in the Smith set.

In a three-cycle, Pb would elect the candidate among the top two who 
beats the other one pairwise - kind of like top-two runoff within the 
Smith set, now that I think of it.

It's possible that in a cycle situation, a party A can split its vote so 
that instead of the Plurality ranking being A>B>C, it becomes B>C>A1>A2, 
and then the clones are kicked off the list early, after which B beats C 
pairwise and wins.

So in a three-cycle, it can be as bad as Plurality (within the Smith 
set) if the clones can't reach second place. Larger cycles will lead to 
more complex behavior: probably not a kind of clone failure you can 
engineer, but one that could happen if the votes just happened to turn 
out right.

It's difficult to tell whether the clone failure would be relevant in 
practice - I tend to prefer just passing the criterion to begin with so 
there's no ambiguity. See my discussion with Richard Fobes - but here I 
don't have that option (yet).

In any event, it's a failure that IRV proponents will use for all that 
it's worth (just like we hold IRV's monotonicity against it).

-km