On Tue, Jul 3, 2012 at 4:03 AM, Juho Laatu <[email protected]> wrote:
> On 3.7.2012, at 3.39, Michael Ossipoff wrote: > > > Yes, even in that small district, d'Hondt's bias will of course make >> things worse for small parties. But d'Hond't effect will be less in the >> small district, even as the small district problem makes things worse, in >> its own way, for small parties. >> >> You said: >> >> >> I simply summed up the expected D'Hondt biases of the multiple districts. >> The biases of small districts may easily sum up to multiple seats per party >> (= higher than with one large district). >> >> > [endquote] > > You're using "bias" with a different definition that its usual definition. > > > I used word "bias" in its general English meaning, in this case referring > to how D'Hondt favours large parties. > > [endquote] Fair enough. I just meant that even the unbiased (with flat probability distribution) Sainte-Lague will give a small party less s/v, when it doesn't give that party any seats. But, say that a small party is equally likely to have its final quotient anywhere between 0 and 1 (and certain to have it in that range); and that a large party is equally likely to have its final quotient anywhere between 99 and 100 (and certain to be in that range). With Sainte-Lague, the small party and the large one have exactly equal expected s/v. That's what I mean when I say that Sainte-Lague is unbiased. The expected s/v is equal, in the way that i described, for all intervals. (again, assuming a flat probability distribution, for finding a state at various population-sizes.) > > > You said: > , > splitting the districts in several small districts is probably > strategically even better for them. > [endquote] > > Not if you're judging the benefit to them in terms of their s/v as > compared to other parties' s/v. > > > If the party leaders are allowed to decide between getting nice s/v values > or getting more seats, I guess they will choose the latter. > > [endquote] But, with a given number of voters, a higher s/v means more seats. > > > In a small district, very small parties will be excluded, who wouldn't be > excluded in an at-large allocation. But the big party will get more seats > in the at-large allocation too. > > > Do you have an example (or a definition) where (in D'Hondt) large parties > are likely to get more seats when a country is divided in larger districts? > > [endquote] No, but it's an unquestionable fact. For two intervals between consecutive integers, n to n+1, and N to N+1, the bigger N is, in comparison to n, the greater is the factor by which the N interval party's expected s/v is greater than the n party's expected s/v. AT large, or in large districts, N can be greater than n by a greater amount, meaning that d'Hondt's bias is greater. That gives more seats to a large party. Mike Ossipoff > > > Juho > > > > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > >
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