[EM] Gerrymandering and PR

Adam Tarr atarr at ecn.purdue.edu
Tue Mar 19 13:05:46 PST 2002

Joe Weinstein wrote and Alex responded:

>>usual PR presumes that voters want to be proportionally
>>represented ONLY according to political party, not other criteria,
>>including geographic proximity.
>Good point about geographical concerns.  In a bicameral state legislature
>it would be reasonable to elect one house by PR and the other with single-
>member districts.  We can debate which house of the legislature should be
>elected by PR, but I think the basic idea is reasonable. 

This is a reasonable way to do things.  You could even guarantee 
proportionality across the state as a whole by having the PR house simply 
balance the total representatives in both houses to match total 
proportionality of the votes.  So if a state is split fifty-fifty between 
Democrats and Republicans in overall voting, but Gerrymandering has made 
the single-district legislature 70% Democrats, then the Republicans will 
get 70% of the seats in the PR house to compensate.  This is roughly how 
Germany does things, right?

This approach forces us to use a party list version of PR in the other 
house.  This isn't really a flaw, except it can raise some 
interesting/confounding implementation questions.  If you use open list PR, 
then do you allow candidates to run in the general list and in individual 
districts?  If not, it creates a tricky strategic question for the 
candidates.  If you use closed list, do you have the voters vote for lists 
at all, or do you just use the results of the district elections to find 

I'd suggest open list, and letting candidates run for both houses.  If they 
win their district election, they are withdrawn from the general race.  
This way the parties have as little control over the candidates as 
possible, thus diffusing the potential for extreme party discipline in the 

This class of methods is still somewhat vulnerable to Gerrymandering, 
however.  The party in control of districting can engineer a small but 
consistent majority in one house, thus virtually insuring at least a split 
of the government.  For this reason I consider this only a partial 

>Also, I think PR
>should stick to districts of 5 or 6 members, rather than operating state-
>wide, to keep the district sizes half-way reasonable.

Whether this is necessary really depends on the election method.  If the 
election is done using open party list, then voting is very simple no 
matter how many candidates there are.

There's a balance that needs to be struck between simplicity and 
proportionality.  The smaller the district, the less proportional it 
becomes.  Five or six seats seems like the bare minimum to insure good 
proportionality.  Looking at Malta's elections shows what a dismal failure 
proportionality can be with less seats per district than that.  On the 
other hand, Australia has 15-seat districts with 5 parties where 95% of 
voters just use the shorthand method and vote a party line, since voting 
for all the candidates is such a pain in the butt.

The voting method figures prominently here.  In closed list, the number of 
seats in the district is totally irrelevant.  In open list, a large 
district is still very manageable.  In PAV, on the other hand, large 
districts get unwieldy pretty quickly.  In STV (or proportional Condorcet 
Voting if that works) they gets unwieldy even faster, since you have to 
actually order the candidates, not just check them off.

>>Also by the way, we would get much better 'PR' using PAV applied to
>>individual candidates, not parties.
>I agree that PAV would provide excellent proportionality while keeping the
>scrutiny on individual candidates.  However, as I understand it, PAV
>requires keeping 2^n tallies when there are n candidates.  In CA there are
>normally 7 parties on the ballot.  If we had 5-member districts that could
>lead to 35 candidates, or 2^35 = 34 billion tallies.  The Florida fiasco
>shows that ballot counting matters, and should be a criterion when
>evaluating election methods of an sort.

Your criticism is accurate.  Any non-summable system, such as STV or PAV, 
gets huge numbers of tallies with large numbers of candidates.  Yet 
Australia uses 15-member districts with STV... and those who don't vote a 
party line have to rank around 75 candidates!  The number of possible 
ballots is 75 factorial, which is a bigger number than any computer could 
handle, really.  If anyone has information on how Australia tallies these 
elections, it could be interesting.  Presumably they count the votes the 
same way a person would... only considering the top vote at any given time.

PAV cannot be simplified this way, since it considers all the votes of any 
ballot at once.  Furthermore, all the ballots need to be considered at once 
to evaluate a potential slate of elected candidates.  So a fairly powerful 
computer is needed to tally the results.  Still, 34 billion (34 thousand 
million) ballot counts is not an impossibly large number.  But in a 75 
candidate district, you get around, oh, 38 septillion (38 thousand million 
million million) ballot counts, which _is_ more or less an impossibly large 

If you want to simplify PAV implementation, you could restrict the voters 
to voting for candidates on one party list only.  Their votes would be 
counted as single votes for their party in a closed party list election, 
and the group of candidates from each party list chosen to fill the seats 
assigned to the party would be determined by PAV elections within the party 
list.  This is a sort of open list/PAV hybrid.  The advantages it has over 
PAV are simplicity for the voter and for the counting of results, and that 
Webster's allocation method can be used for the party lists if desired.

One last note on this subject.  From the voter's perspective, there are 
lots of clever methods we can dream up to make voting in large-candidate 
districts easier.  I posted a while back about a scheme where STV voters 
could vote for candidates and lists of candidates in any mix.  If you have 
touch-screen ballots (growing in popularity in places like Florida) then 
PAV could be easily implemented... for example, "touch this box to 
highlight the following ten candidates, and touch any candidate to 
highlight or un-highlight him/her."

>To keep the counting simple while keeping the scrutiny on individuals, I
>am intrigued by Cumulative Voting.  STV, with n! tallies, is clearly out
>of the question.  Some party list systems may also have potential.

If the most simple system is called for, then I would go for open party 
list.  I think this does better on proportionality than cumulative voting, 
and it is even easier for the voter (just vote for your favorite 


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