# [EM] average over time proportionality election method

raphfrk at netscape.net raphfrk at netscape.net
Sun Mar 5 23:04:03 PST 2006

```>Very interesting idea! Reminds me of Ebay :-)
>But:
>> This leads to the long term average number of seats
>> for the candidate matching the candidate's proportion of votes.
>Can you prove this? Seems not so obvious to me...

It is based on the assumption that the "cost" in votes to get elected
is roughly the same in every election.  If it always costs 1000 votes
to get elected and a candiate gets 300 votes, the candidate is 30% of
the way to get a seat.

In the simulated elections, the cost to get elected was:

182
661
619
777
952
1004
819
839
751
906

There is a ramp-up when the system is started as no low popularity
candidates would have had a chance to build up votes.  This gives large
popularity candidates a few "cheap" seats.

Also, differences in voter turnout from election to election affect how
many votes needed to get elected.  If a candidate gets elected in a
high turnout election, then the candidate will use up more votes to get
elected.

However, even with +/-50% differences in voter turnout, the number of
votes needed to get elected in each election changed by a smaller
amount.

Another option would be to force the number to be constant.  If the
highest candidate in the election didn't have the required number of
votes, then no candidate would end up with a vote "debt" or no
candidate would be elected from the district.  This could be combined
with it being possible for 1 district to elect more than one candidate.

I think if the system was used in a multi seat district, the cost to
get elected would be pretty constant anyway, so wouldn't need to be
forced.

In any case, the system ensures that there is no wasted votes.  Finite
lifetimes of candidates and voters would pose a limit though, there is
little point in casting a vote that won't take effect until 100 years
after you (and the candidate) are dead.

One issue is that replacing an incumbent would be a multi election
thing.  Voting for a popular candidate who isn't the incumbent would
still have the spoiler effect in that one election splitting the party
vote.  It would balance out in later elections.  Again, multi seat
districts would help with this.
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