[EM] Multiwinner Bucklin - proportional, summable (n^3), monotonic (if fully-enough ranked)

[C.Benham]

Jameson Quinn wrote (28 March 2010):

> >/ What does "MCV" stand for? />/ /
>
> Ooops. I garbled your term, didn't I? It's supposed to be Majority 
> Choice Approval, not Majority Choice Voting. 


"Majority Choice Approval"  was invented and introduced a few years ago 
by Forest Simmons, and I think he
coined the term.

For a short time I endorsed it as something simple that meets  Favorite 
Betrayal,  the "voted 3-slot ballot version"
of Majority for Solid Coalitions and Mono-raise.

> >/ Does "top-two runoffs" mean a second trip to the polls? />/
> /
> Yes. I regard this as an advantage. If the situation is divisive 
> enough to prevent a majority choice in two rounds of approval,
> then a further period of campaigning is a healthy thing. It's the only 
> way to guarantee a majority. (I don't think that mandating
> full ranking counts as a true majority).
>
> / />/ How are the candidates scored to determine the top two? Is it 
> based on the  //candidates' scores after the second
> > Bucklin round? >
>
> // /That's the simplest answer, and I'd support it. It's also the best 
> answer with honest voters. Actually, the best answer for
> discouraging strategy is to use the two first-round winners. That 
> tends to discourage strategic bullet voting, since expanding
> your second-round approval can not keep your favorite candidate from a 
> runoff. 


Unfortunately these top-two runoff versions break MCA's compliance with 
Favorite Betrayal and Mono-raise.

Top-rating your favourite F could cause F to displace your compromise C 
in the runoff with your greater-evil E, and then F loses
to E when C would have beaten E.

Also, like plain Approval followed by a runoff between the two most 
approved candidates, it is *very* vulnerable to "turkey-raising"
Push-over strategy. Voters who are fairly confident that their favourite 
can get into the final runoff have an incentive to also approve
(or top-rate, depending on the version) all the candidates they are 
confident their favourite can pairwise beat in the runoff.

The Push-over incentive is stronger than it is in normal  TTR, because 
the strategists don't have to abandon their favourite in the first
round (and so taking a much greater risk, if there are too many trying 
the strategy, of  their favourite not getting  into the final without
their votes when without their strategising their favourite would have 
got into the second round and won it).

Also some people might object that parties that run a pair of clones 
have an advantage over parties that run a single candidate.

 From your (Jameson's) earlier (26 March 2010) message, I gather you 
consider "likely to elect the CW" a big positive.
For something simple then, why not  "3-slot Condorcet//Approval"?

*Voters give each candidate a Top, Middle or Bottom rating. Default 
rating is Bottom.
If one candidate X  (based on these maybe constrained ballots)  pairwise 
beats all others, elect X.
Otherwise, interpreting Top and Middle rating as approval, elect the 
most approved candidate.*

Chris Benham

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