[EM] STV district magnitude

James Gilmour jgilmour at globalnet.co.uk
Thu Jul 17 08:33:03 PDT 2003

I wrote:
> > But if we are looking
> >at a national parliament of, say, 120 members, it  would be 
> undesirable
> >to elect all 120 from a single national-district.  The 
> principal reason
> >is not one of practicality, but rather political consequence.
> >Experience has shown that it is politically undesirable to give
> >representation down to 1 in 120, as the example of the Israel Knesset
> >shows.  In countries using party list systems of PR with national
> >aggregation of votes to determine the parties' shares of seats, it is
> >common to apply an arbitrary threshold (typically 5%) specifically to
> >exclude small parties.  These thresholds are arbitrary (Why 
> 5%?  Why not
> >4% or 6%?); it would be more logical to accept the de facto 
> thresholds
> >that come with districts - where the sizes of the districts have been
> >determined for other, logical reasons.
> >
> >For this reason I would reject all "extensions" of STV-PR 
> that seek to
> >add any aggregation of votes across districts with the aim of
> >"improving" the PR. 

James Green-Armytage asked:
> 	What it it about the Israeli parliament which proves 
> that high district
> magnitude is a mistake in general?

Israel uses closed party list in one national district.  This is the
worst possible combination of all PR systems.  Any group that can secure
1/120th of the national vote will get a seat in the Knesset.  This give
representation to very small groups which makes it possible for the
extremes of the political spectrum to gain representation.  The system
does not encourage them to seek any accommodation with those of less
extreme views.  Allied to this is the effect WITHIN parties of the
closed list.  The candidates of a minority faction within a party may be
included on the party's list to ensure that the faction's supporters
vote for the party, but those candidates will be placed well down the
closed list so that they have no chance of election.  To overcome this,
the faction splits off to form its own party, when its candidates will,
of course, be at the top of its own list.  If it can secure at least
1/120th of the national vote, it will get at least one of its candidates
elected.  This is what has happened over many years in Israel.

The political consequences are there for all to see.  Many small parties
are represented in the Knesset, many with extreme views (ie extremely
different from one another).  Coalition building has been very difficult
to the point of near impossibility at times.  When a coalition
government with a small majority wants to take a difficult decision on
some of the very difficult issues that face all governments in that part
of the world, one or more of the extreme parties threatens to bring down
the coalition.  This gives the extreme parties power greatly in excess
of their support among the electorate.  This makes government very
difficult.  It could even be considered a denial of democracy as these
tiny minorities may be frustrating the wishes of the majority of
electors.  Certainly the voting system gives them no incentive to seek
consensus on the way forward.

> >The law of diminishing returns applies to representation in much the
> >same way as it applies to many other things.  As the number 
> of members
> >per district rises, the proportion of voters NOT guaranteed
> >representation falls off very rapidly at first and then progressively
> >more slowly.  (This applies to all systems of PR, not just STV-PR.) 

> 	What are your grounds for saying that there is a 
> diminishing return of
> representativeness with greater district magnitude?

I did not say this.  The law of diminishing returns states that for each
successive equal increment of input the successive increments of output
become smaller.  Of course, the total output increases as the total
input increases, but the law of diminishing returns relates to the
relative increments.

In the case of district magnitude, if we increase the number of members
from 3 to 4 (an increase of 1), the proportion of voters not guaranteed
representation by STV-PR (Droop quota) falls from 25% to 20%, a decrease
of 5.  But if we increase the number of members from 10 to 11 (also an
increase of 1), the proportion of unrepresented voters falls from 9% to
8%, a decrease of only 1.

I have a graph that shows this extremely well, but have yet to find
somewhere I can post it with public access.  (I asked if there was a
FILES archive on this List, but no one has replied.)  

> 	I agree that this might be the case if you just measure 
> whether someone
> is represented by whether they get a seat for the party they 
> like best,
> but I believe that voters' true preferences are more complex 
> than just a
> choice of one party or another, and so I'd say that there is 
> always room
> for representativeness to keep increasing at the same rate.

Views about where to settle on the diminishing returns curve will
differ, but the diminishing benefit of each successive increment in
district magnitude should be taken into account in considering the
trade-off with the other factors that pull in the opposite direction.

> 	You have to consider that there might be some ideas or 
> groupings that are
> very important to people, but are never concentrated enough to have a
> tenth of voter preferences.

But do real voters in real elections mark enough preferences for this to
come through?  See, for example, my tabulation from the Meath
constituency in Dail 2002 election, posted on 9 July.
> >There is also a trade-off between the proportionality of 
> representation
> >and the localness of representation.  These two factors pull 
> strongly in
> >opposite directions so far as optimal district size is concerned.  In
> >some political cultures, real electors attach great importance to
> >localness and so it cannot not be ignored. 
> 	I agree that this is a tradeoff. It seems to me the 
> most important
> tradeoff by far.
> 	Again, electing some candidates in smaller districts 
> and others in larger
> districts that encompass the smaller districts is a method of 
> having it
> both ways. They could either be part of the same legislative 
> chamber, or
> they can form two separate chambers. If nobody wants this, then people
> just have to decide on a middle-ground. Maybe they should use 
> Condorcet to
> decide. : )
> 	Actually, the only way of meeting both of these desires 
> at once is to
> have a legislature that is just bloody huge. I'm not 
> especially in favor
> of that, but it is worth mentioning.

I don't see that the legislature has to be large.  Potential district
magnitude MAY be one factor to consider when deciding the size, but it
is certainly not the most important.  I certainly see no grounds for
suggesting that members elected from large districts should sit in one
chamber of the legislature while those elected from the smaller
districts should sit in a different chamber.  First decide whether you
want one chamber or two.  If you have two, then decide the appropriate
district magnitude for the election of each of the two chambers.

As I've already indicated in earlier posts, I am prepared to accept
great flexibility in district magnitude within any one legislature,
provided there is a sound rational for the variation.  I am also
prepared to vary the numbers of electors per elected member, in addition
to varying the numbers of members per district.  I know this is greeted
with horror by many "PR purists", but I live in the real world and know
what real people want, at least here in Scotland.  It is a compromise
and those who are working for practical reform should be prepared to
recognise that.


I am not in a position to comment on your views of the political culture
in the USA.  What you said does, however, emphasise the importance of
taking the political culture into account when considering which voting
system will secure the "best" representation for the electors.


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