[EM] Sainte-Lague vs d'Hondt for party list PR

[Juho Laatu]

On 2.7.2012, at 1.51, Michael Ossipoff wrote:

> I always advocatred SL (Sainte-Lague) over dH (d'Hondt) for party list PR, because, if you're using PR it's because you want proportionality,  and if you want proportionality, then you want SL.
>  
> Then, more recently, I said that, since I don't think that we need PR anyway (though I have nothing against PR), d'Hondt would be fine, especially since it guarantees a seat majority to a vote majority.
>  
> But now I feel that I was mistaken to say that. For two reasons:
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> 1. For fair inclusion, there should be no threshold. d'Hondt will disproportionately exclude small parties. That matters, because PR can only be justified, in comparison to a good single-winner method, if there's no significant split-vote problem. You shouldn't have to worry that you need to vote for a compromise because your favorite party might not have enough votes to win a seat. That problem is, of course, worse in d'Hondt than in Sainte-Lague.
>  
> 2. In PR, the idea is that you don't have to compromise in your voting, because you can just elect representatives (members of parliament congress-members, etc.) of your party to parliament or congress, and _they_ can do the compromising, when necessary--but only when necessary.
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> But how true is that in d'Hondt? Not very.
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> Say your favorite party is significantly smaller than the ones that are in major contention in parliamentary voting. If you vote for your party, and it's a small party, d'Hondt will give it _significantly_ less representation per person, as compared to the larger parties.

D'Hondt favours large parties. But if you assume that PR will be calculated at national level, D'Hondt favours large parties only in the allocation of the last fractional seats (the last possible seat for each party). If the results are counted separately for each district, the bias in favour of large parties becomes bigger.

If you want to get rid of the problem of voting for a party that will not get any representatives, you could allow the vote to be inherited by some other party one way or another (e.g. second preference in the ballot, or tree structure of the parties). But for most purposes already methods that guarantee a small party its first seat if it gets 1/N of the total votes (where N is th number of seats) may be good enough (people may not fear too much losing their vote when they vote for the small parties). Most real life electoral systems have higher bias anyway for various other reasons like thresholds or not counting PR at national level.

> So your favorite party won;t have many seats with which to support coalitions. If compromising, coalition-support, are necessary, then you'd do better, in the d'Hondt PR election, to give your vote to a big party, so that you can thereby add more seats to the coalition that you want to support.
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> That's no good. d'Hondt fails FBC, if FBC were extended to PR methods.

What would that extended definition say?

Juho