[EM] Apportionment and minimum desirable legislature size?

[Abd ul-Rahman Lomax]

At 08:03 PM 4/18/2011, Alex Small wrote:
>I've been following some of the apportionment threads, and wanted to 
>pose a related question:  Is there an optimal legislature size from 
>the standpoint of apportionment?

The very concept of apportionment to districts militates against 
optimal size, when combined with an idea of proportional 
representation, if the district sizes vary greatly.

The purpose of representative democracy, as distinct from direct 
democracy, is to create a representative body of a manageable size, 
because the difficulty of deliberation increases, probablly with the 
square of the size. Large bodies, such as the U.S. House, and even 
smaller bodies, already effectively do this with committees.

>Let's say that you decide to apportion seats among 
>constituencies.  We'll leave aside the issue of whether those 
>constituencies will elect their representatives from districts 
>within the constituencies or proportionally in an at-large election 
>or whatever.

It is possible to elect a PR legislature with no fixed 
constituencies, but with most seats having a defined geographical 
district. Some seats might represent the entire state. Others might 
represent relatively small but populous districts.

>   We'll just stipulate that each constituency gets at least one 
> seat, and that the number they get is roughly linear in their population.

So this depends on prior division into "constituencies." If we toss 
that division, but allow constituencies to form as part of the 
election process -- and this is exactly what Asset Voting could do -- 
we can end up with *exact* proportionality. Every seat represents the 
same number of voters.

With Asset, as well, voters would know exactly -- or quite closely -- 
which seat their vote elected. (This would happen if electors -- 
candidates holding unused votes -- assign the votes according to the 
precincts they came from, preferring to assign them in a block, or 
"trading" such assignments, so that an elected seat does represent a 
mostly coherent geographical district.)

>The common way to do this is you start off with each constituency 
>having 1 seat, and then you hand out the remaining seats 
>one-at-a-time based on some formula.  Different people have proposed 
>different formulas, either based on who is most under-represented at 
>the moment, or who would be least over-represented with an extra 
>seat, or whatever, but regardless of what formula you use, let's 
>just agree that the method goes one-at-a-time.

It's all based on a model which guarantees lack of proportionality.

Asset simply allows "electors" -- those holding votes cast in a 
presumably secret ballot election -- to reassign the votes to create 
seats. This is not an adversarial process, there are no "losers," 
only winners, determined as a quota of votes are assigned.

If it's the Hare quota, there is no error, but there is increasing 
pressure for those holding "dregs" to compromise. I've suggested that 
failure to compromise result in a natural consequence, loss of 
representation pending a compromise, and I'd allow seats to be 
created at any time, up to the next election. It is also possible to 
have a hybrid direct/representative legislature that routinely 
operates through elected seats, but which still allows electors -- 
who become "public voters," representing all who voted for them -- to 
cast direct votes.

Pure, total, complete representative democracy, with everyone 
represented who cares to be. I don't know of any other method that 
approaches this.

>The first few seats will mostly go to the largest 
>constituencies.  So, if you have 50 states with a broad distribution 
>of populations, and you have a legislative chamber with 60 seats, 
>most of your states will be under-represented.  If you expand to 
>1000 seats or whatever, your biggest disproportionality problem will 
>probably be at the low end of the scale, i.e. adding or removing 1 
>seat from a state with 5 representatives changes the ratio of reps 
>to population by 20%, while adding or removing 1 seat from a state 
>with 100 reps changes the ratio of reps to population by 1%.

I think we get way ahead of ourselves. Until we adopt advanced voting 
systems in small organizations, and in organizations of increasing 
size, we are unlikely to see major political applications.

>If your only concern is numerical fairness, of course, you should 
>just keep adding more seats, until you reach something like the 
>square root of the population.  But if you want to keep your 
>legislature size low for practical reasons (i.e. in the 3 digit 
>range), is there any good quantitative criterion for minimum size?

Size can actually be determined on-the-fly. Ultimately, with hybrid 
direct/representative Asset, the optimal size becomes a matter of 
operational efficiency, because the electoral structure can become a 
penumbra, a large standing body that *fully represents the 
electorate*, but that structures itself into smaller bodies as 
needed. It really would be Delegable Proxy, in this penumbra.

>My intuition tells me that either there is no fundamental criterion 
>here, but a practical one is to keep adding until most of the 
>changes are in the median state.  Or keep adding until the ratio of 
>population to reps for the median state equals the ratio of 
>population to reps for the largest state, plus or minus some small 
>tolerance that you decide on.
>
>Anybody have ideas for formalizing this issue?

Just be aware that you are putting lipstick on a pig.

I am not represented because my district is represented. My district 
is represented, not me. The best single-winner election methods can't 
fix this. Nor can ordinary multiwinner methods, they merely 
ameliorate the problem a little. Asset is a trick: it's not an 
"election method," by most definitions, it is not deterministic, it 
is deliberative in character.

Let me put it another way: it's intelligent.