[pp.int.general] One good, one bad

[Boris Turovskiy]

Jeremy Morton wrote:
>> A direct proportionality between population and votes does (most
>> probably) not lead to the votes having equal power :)
>
> Would you care to explain why?  Because this seems to me to be the 
> definition of the votes having equal power.
Simple example: We have 2 states with populations 50 and 30 which get 5 
and 3 seats, respectively, and 2 parties. Now combinatorically, a vote 
has (in one of the models) a chance of being the decisive vote in 
~1/sqrt(N) cases. Thus if the seats are proportional to N, the voter's 
influence on seat distribution will be proportional to N/sqrt(N) = 
sqrt(N), so the bigger the state, the more influence on seat 
distribution each voter there has. There are more elaborate (and less 
substantiated) models that propose logarithmic and other kinds of 
proportionality, but all agree that it should be less than a direct one.
The other aspect is that seat distribution is different from power 
distribution (best example in a parliament - of 2 parties having 51% and 
49% the first has 100% power and the second one has zero, when it comes 
to majority decisions).

Best regards,
Boris