[EM] 120 Seats

Abd ul-Rahman Lomax abd at lomaxdesign.com
Mon Apr 17 07:58:31 PDT 2006

At 05:41 PM 4/16/2006, Doreen Dotan wrote:
>There seems to be a large number of parliaments and legislatures 
>that are composed of 120 seats in countries that are very dissimilar 
>demographically, politically, economically, geographically and so 
>on.... Is the number 120 significant because of the particular 
>mathematical properties of the number 120, to wit:
>120 is the <http://en.wikipedia.org/wiki/Factorial>factorial of 5.

This one is probably a factor in the choice of that number. The rest 
of the mathematical properties would not be relevant, in my opinion. 
If there are terms and set election cycles, where a fraction of the 
representatives are elected in each cycle, which is desirable for 
stability and continuity, presumably the fraction is the same for 
each cycle and must therefore be of the form 1/N times the total 
number of representatives. So the total number must be divisible by 
N, which limits the total number to a composite number.

Very large bodies are known to be highly inefficient. Such large 
bodies as exist and are other than dysfunctional actually break 
themselves up into a set of smaller bodies for most business....

120 is a compromise between efficiency and diversity. In a peer 
assembly, where every member has the same voting power, the total 
number of representatives must be relatively large in order to 
include small factions, 100 as a total allows a coherent faction of 
1% to be represented.

However, this is a restriction of the artificial constraint of having 
a peer assembly. Proxy assemblies would not have that restriction, 
and could be far smaller, and thus more efficient, while allowing 
much smaller factions to be represented. If there are N members, 
presumably some would represent more than 1/N constituents -- we call 
them "clients" -- and therefore some could represent less than 1/N.

As was pointed out, PR systems generally waste a certain number of 
votes, leaving a fraction of the electorate unrepresented. While it 
might seem that this fraction is at most approximately 1/N, the fact 
is that there could be many coherent factions smaller than 1/N; the 
result with a fixed assembly size, on a surface analysis, would seem 
to be that more than 1/N of the electorate can be unrepresented in a 
peer assembly of N representatives.

Asset Voting, however, resolves this problem to a large degree. Asset 
Voting used to create a peer assembly potentially leaves no wasted 
votes. A brief explanation is in order: Asset Voting allows votes 
received by candidates to be considered "assets" which can be 
redistributed by the candidates as necessary to create winners. A 
winner "consumes" by being elected, the quota of votes, leaving the 
rest of the votes received, if any over quota, to be distributed by a 
winner to other candidates. If a candidate receives less than the 
quota, that candidate can still be elected if he or she receives 
enough votes from other candidates, or can cause the election of a 
chosen candidate by providing that candidate with all or a portion of 
votes received.

Asset Voting is a form of proxy voting used as an election method. 
The candidates are proxies. If candidates are restricted to 
redistributing their votes to a single candidate, who then 
redistributes any excess, this is Delegable Proxy.

The original Asset Voting proposal, by Warren Smith, allowed voters 
to assign a fractional vote to candidates, with the restriction that 
the sum of votes assigned did not exceed one. It has been pointed out 
that this restriction is unnecessary, if the ballot result is 
normalized to unity sum, leading to a very simple form of Asset 
Voting: FAAV, Fractional Approval Asset Voting, where voters vote for 
candidates using a normal plurality-style ballot, as many as they 
choose "Approve", with multiple votes, if any, being reduced to 
fractions. Thus the voter either assigns his or her vote to a single 
candidate, or to a virtual committee. I personally don't see a need 
for such committees, except that allowing this kind of voting 
eliminates ballot spoiling due to overvoting, and there is no harm in 
it except for counting complication. If the counting complication is 
considered too much of a problem, then standard plurality rules could apply.

But the method is not "plurality," because of the allowed 
redistribution of votes. Winners must receive, not a plurality, but 
the quota (which in a single-winner election would presumably be the 
smallest integer greater than 50%).

The system would need to address refusal of candidates to 
redistribute votes. Such a refusal quite properly would result in 
election failure, not in the election of some candidate with less 
than the quota, which would reward such intransigency. In a 
relatively large assembly, Asset Voting allows even very small 
factions to be represented, not directly, but by a winner who has 
agreed to at least present their views and to represent, to the 
degree possible and consistent with the winner's own positions, their 
interests. Thus Asset Voting, in my view, is as perfect as is 
possible with a peer assembly, without going to proxy voting in the 
assembly itself.

(Note that many assemblies allow proxy voting at least under some 
conditions. I listen to NPR radio from a New York station, where 
there is common mention of proxy voting by representatives in the New 
York House, in committee. It's considered a bad idea by some, but, in 
my view, it is only a bad idea if "proxy voting" allows a proxy to 
cast a vote *different* from the proxy's own vote, as instructed by 
the giver of the proxy. This, then, allows votes to be cast remotely, 
with no participation in the deliberative process, which, yes, is a 
very bad idea. Indeed, this is a general problem with public, secret 
ballot elections, which invite votes from people who have no 
participation in deliberation. I think such votes should be limited 
to consent votes, not to active initiatives which take the place of 
legislative deliberation. Indeed, my opinion is that elections in 
general are problematic. I prefer the right to choose who represents 
me without being restricted, in any way, by the votes of others.)

http://metaparty.beyondpolitics.org is a new effort by Jan Kok, 
worthy of attention.

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