[EM] STV district magnitude

James Green-Armytage jarmyta at antioch-college.edu
Thu Jul 17 12:35:02 PDT 2003

Dear James Gilmour and other election methods fans,

	This is my response to James Gilmour's response to my posting. I hope
that it is not unreadable. I think that all of the writing that is not
proceeded by little carrot-brackets on the left or highlighted in gray is
my current response, that is, new material. Anything with the carrots or
the gray is either James Gilmour's writing or, less common, my own writing
from the last post...

>Israel uses closed party list in one national district.  This is the
>worst possible combination of all PR systems.  

	I agree that closed list is a bad idea, but I don't agree that nationwide
list is a bad idea, especially in a small country like Israel.

>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. 

	This might be one of the main points that we disagree on. Personally, I
have no desire to exclude the "extremes of the political spectrum" from
having seats in the legislature, provided that they have no more seats
than they deserve in terms of their proportion of the vote.
	I thought that that was pretty much the main purpose of proportional
representation: to allow minority political views into the discussion at
the highest levels of government.
	I refuse to make the value judgement such that if a political view is
only supported by 1/120th of the people in a state, that view is
automatically invalid, "extremist", or wrong.
	Do you really disagree with this? This is more of a value judgement than
a factual or causal statement, but it is possible to discuss it if our
disagreement is stemming from this point.
>The system
>does not encourage them to seek any accommodation with those of less
>extreme views.

>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.

	I have already expressed my confusion with and distaste for parliamentary
systems where coalition majorities need to maintain some kind of formal
cohesion lest the whole government come crashing down. (That was in the
July 16 STV district magnitude which got me into this thread in the first
place. By the way James, I would appreciate your reading that, if you
haven't already, since it is really the same topic.) 
	I agree that the combination of such a parliamentary government system
and a highly proportional voting system could be chaotic / screwy. But I
really think that the part that is causing the trouble is the
parliamentary government part.
	If a small party is needed to form a majority coalition, and if their
withdrawal from that coalition causes a costly and tumultuous change in
government, then I agree that something is wrong. 
	But instead of trying to squelch small parties, why not change the system
to allow for parties and individual candidates to vote sometimes in the
majority and sometimes in the minority, without having the government fall
	That is, a system that allows for shifting alliances which wouldn't
really be alliances but really just agreements and disagreements on
particular legislation, while having a structure that allows for some kind
of over-arching stability at the same time, such as an executive with a
fixed term that can't be cut short by a vote of no confidence. 
	(Of course there could be a sort of impeachment procedure like we have in
the US in case the executive does something really illegal, and they could
always resign at will... just so long as a simple legislative majority
isn't sufficient to topple them.)

	In the absence of coalition-toppling threats, I would argue that PR
systems definitely *do* encourage small parties to "seek accommodation
with those of less extreme views". (Or, to be less judgmental: 'more
popular views'.)
	No party with 2 or 3 of 120 seats is going to pass any legislation on
their own, of course. How could they avoid compromising with larger
parties and more mainstream views? 
	In fact, the process of strong PR encourages such compromise more than
any other method of representation, because such small minorities actually
do get seats at the table. That way, they are given an outlet to engage
with the other political parties, rather than just being totally excluded
and maintaining their subculture as a permanent disconnect from the rest
of the political scene.

>> 	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.

	I don't think that I misunderstood you here. I understand the law of
diminishing returns from economics; I know that it is not a decreasing
output with increased input, but rather a decreasing marginal output with
increased input. Or, a decrease in the fraction of the additional output
divided by the additional input. Anyway, we're on the same page at this

>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.)
>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.

	I looked at the chart, and I understand the point you are trying to make,
but I don't think that I agree with you, and I don't think that you
understood the point that I made in return.
	First of all, your chart says that in a one seat election, 50% of the
voters are guaranteed representation. 
	My point is that there are different degrees of representation. Is the
winning candidate necessarily the first choice of 50% of the electorate?
Of course not. Do those 50%+ really agree with everything that candidate
does? Of course not. 
	Sooner or later, 50%+ of the ballots got transferred to one candidate,
but that candidate does not necessarily represent all of those voters very
	There are different degrees of representativeness. There is
representativeness that is rather vague, and there is representativeness
that is more specific. The only way for a person to be totally, completely
represented in parliament is if they have a seat there themself. The rest
is all a matter of degree. A matter of how close one's views are to the
views of one's closest representative in the legislature?
	My point is that if you measure it this way, there is probably *no*
diminishing return given higher district magnitude. Does that make sense?
	At least I have made the point that your evidence for a law of
diminishing returns depends on a very weak definition of

>I don't see that the legislature has to be large. 

	My point was that, yes, district magnitude and locality do pull in
opposite directions, as you said, but *only* if you assume that the size
of the legislature is constant. That is, you can increase both district
magnitude and locality at the same time, but as a result, the total size
of your legislature will increase.
	I agree that there is a point where a legislature can so big as to be
unwieldy. I'm not advocating big legislatures, I was just making a point
that those two variables only pull in opposite directions given constant
total seats.
	So, this is the serious tradeoff in district magnitude as far as I'm
concerned: it is between locality, representativeness, and total size.

>> 	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.

	Yes, they would definitely mark enough preferences, because the
candidates who are closest to them and share the ideas most important to
them will be the ones whom they rank first. (Unless there is a situation
where favorite betrayal is encouraged, which is a problem that can only be
solved through further refinement of the STV system used, etc.)
	The question is more a matter of whether a candidate will run who shares
those ideas and successfully expresses them. This is more likely to happen
with greater district magnitude, and with a refined STV system.

>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. 

	If you mean for example having one 10 member district with 1,000 people,
and another 10 member district with 3,000 people, then this is obviously
unfair, as the 1,000 people have three times more representation per
person than the 3,000 people.
	I can imagine plenty of real people who would want to vote in the 1,000
person district, but any rational person in the 3,000 person district
would prefer that they get 30 representatives rather than 10, and it would
be fair for them to demand this.
	I realize that this kind of disproportionality is common in national
governments, but in normative terms, I think that it is obviously bad. 
	The US senate for example, has 2 senators for every state, even though
some states have dozens of times the populations of other states. For this
reason, it is very hard for me to see the senate as a legitimately
democratic governing body.
	Perhaps this is not the most important topic for us to discuss, though,
since the unfairness of this sort of disproportionality is obvious, and I
recognize that there may be some circumstances where this kind of
unfairness worth it in terms of the positive value of some other reform.

Thank you for your reply.
All the best,
	James Green-Armytage

More information about the Election-Methods mailing list