[EM] the responsiveness of Condorcet

James Green-Armytage jarmyta at antioch-college.edu
Wed Jul 9 09:50:03 PDT 2003

John Hodges wrote:
>Another point: Assume Condorcet-plus-some-completion-method; instead 
>of two-party dominance, should we fear one-party dominance? Condorcet 
>methods strongly tend to pick centrists. Could one party stake out 
>the center and sit on it, unassailable? Or perhaps, might we see a 
>competition of several "center" parties each vying to be 
>indistinguishable from the others, so we routinely have a choice 
>between Coke and Pepsi?

David Gamble wrote:
>Now to what could happen with Condorcet in practice. Condorcet favours
>centrist candidates and parties, in my opinion to too great a degree.
>Under Condorcet a centrist party would be very difficult to defeat.
>Swapping the Democrat/Republican duopoly for a centrist monopoly would
>not be good.  Effective one party states (like Mexico and India were for
>decades) are generally a bad thing. Periodic change in government is
>necessary for a healthy democracy. The Democrat/ Republican duopoly bears
>testimony to the dangers of excessive stability and stagnation.

I (James Green-Armytage) reply: 

Dear John, David, and other election methods fans,
	I like it when criticisms of Condorcet take me by surprise. I doubt that
I would have ever considered that Condorcet might lead to a stagnating
single party dominance. Actually, I really don't think that it would do
this, but at least the idea forced me to think for awhile in order to
justify my intuition. This was what was on my mind as I watched the
fireworks the other day. Here is what I came up with.

	Of my two major points, let me start with the less important, but simpler
point: spatial variation. Let's assume, for example, that we are talking
about using Condorcet's method for congressional elections in America.
Whenever either Republicans or Democrats have a clear majority in a
congressional district, rather than just a plurality, they will win
Condorcet just fine. The "center" party will not win.
	More generally, the political center (median voters' will) varies
significantly from district to district. Any "centrist" party that ran a
candidate in the exact political center of each district couldn't possibly
have a consistent platform, couldn't have a unified stance on issues,
wouldn't consistently vote with each other on legislation, and therefore
couldn't be called a party in any functional sense of the word. 
	(Unless, of course, they lied in each of their campaigns, and then voted
together in spite of their earlier promises. But if they do that, they
should be ousted anyway. If voters aren't well-educated enough to oust
b.s. candidates like that, then it doesn't matter what electoral system we
use: we're screwed anyway.)
	So, in terms of congress, the more likely result is that you would have a
mixture of Republican-type candidates from the majority conservative
districts, Democrat-type candidates from the majority liberal districts,
and centrist-type candidates from the evenly split districts. The range of
variation would obviously not be as extreme as if you used proportional
representation (which, again, I would prefer, but I will save that issue
for later), but I would imagine that it would be at least as varied as
with plurality or IRV, and probably more so. The reason I say more is that
the people of a given district would have more power to express particular
issues and values that happen to have majority support there, rather than
settling for a very vague approximation of their political views. (If you
don't believe me that Condorcet helps give voters this power, then please
keep reading, I will go further into that idea.)

	Okay, that's the idea of spatial variation, which applies to the
legislature (majority control of which is obviously necessary for a "one
party state.") 
	Much more important, though, is the idea of *responsiveness*. I imagine
that I may repeat this again and again if I keep posting here, but my love
affair with Condorcet is based on the belief that it is the most
responsive method available. That is, it allows several candidates to
genuinely compete, it is most sensitive to subtle changes and preferences
in the electorate, and thus holds politicians very highly accountable to
the will of the voters, not just in terms of a one-dimensional political
spectrum, but with regard to a potentially infinite range of issues and
	This point may be a little too big for me to cover in full here, but let
me just try to approach it as it touches on the issue at hand: that is,
the possibility of dominance by a single, stagnant, center party.
	I worked out two examples, based on slightly different kinds of
responsiveness. One is a shift in the electorate that isn't respective to
a political spectrum ("vertical responsiveness", if you will), and the
other is a shift in the electorate that is respective to a political
spectrum ("horizontal responsiveness", or whatever). 
	I will start with the example of vertical responsiveness. This is an
imaginary sequence of multiple elections using Condorcet's method. First,
Democrats have a slender majority over Republicans. Second, a centrist
candidate enters the running and wins. Third, another centrist candidate
enters the running and beats the first centrist candidate. The idea is
that although the first centrist candidate had found a fruitful middle
ground between the two old parties, s/he is by no means "unassailable".
Although the first centrist was generally right in terms of the general
political median, the second centrist is too, and s/he is more preferred,
for whatever reason. Maybe s/he is just sharper, or more likeable, or
seems more effective in one way or another. Maybe s/he has a stance on an
issue that is preferred equally by members of both sides of the spectrum.

	By the way, I'd like to think that these are relatively "natural
examples", which haven't been heavily contrived to prove my point. I made
up these examples based on what I thought was a plausible outcome within
the bounds of simplicity; I didn't have to discard any examples because
they didn't work out the way I wanted them to. The fact that they are
natural examples is also part of the reason that they are fairly detailed
/ complicated. These examples are not so much intended to *prove* any
point, but more so just to illustrate what the heck I'm talking about with
concrete numbers. If you understand the ideas anyway, then feel free to
skip over the numbers.
	Anyway, here's the sequence. (When I do these examples for myself I have
the first place votes for each candidate surrounded by crazy little arrows
indicating the pathways taken by later preferences. It's far more
intelligible to me that way, but it will be easier to enter it in the
computer using the standard format.)

49: Republican
51: Democrat

	Obviously the Democrat wins this using any sane election method.

39: Republican, Centrist 1, Democrat
10: Centrist 1, Republican, Democrat
10: Centrist 1, Democrat, Republican
41: Democrat, Centrist 1, Republican

	Centrist 1 is a clear Condorcet winner. The Democrat wins using IRV, of
course, but I'm not focusing on that at the moment.

13: Republican, Centrist 1, Centrist 2, Democrat
21: Republican, Centrist 2, Centrist 1, Democrat
5: Republican
	(39 total Republican first)
5: Centrist 1, Centrist 2, Republican, Democrat
5: Centrist 1, Centrist 2, Republican, Democrat
1: Centrist 1
	(11 total Centrist 1 first)
4: Centrist 2, Centrist 1, Republican, Democrat
4: Centrist 2, Centrist 1, Democrat, Republican
1: Centrist 2
	(9 total Centrist 2 first)
14: Democrat, Centrist 1, Centrist 2, Republican
22: Democrat, Centrist 2, Centrist 1, Republican
5: Democrat
	(41 total Democrat first)

	Centrist 2 is a clear Condorcet winner in this case. The example is just
intended to work through the idea that it is not particularly hard for
this kind of supplanting to happen using Condorcet. That is, Condorcet has
very good vertical responsiveness; it can adeptly respond by giving the
victory to a candidate with a similar position on the political spectrum,
but who is more liked overall. This is an all-important quality if you are
interested in having high-quality / well-liked politicians running things,
rather than people who have simply positioned themselves well
ideologically-strategically but are not really all that special in
themselves. Or just if you are interested in political policies or reforms
or ideas that are just generally good and popular, rather than being
especially favored by one 'side' or the other.

	The second sequence is supposed to illustrate that Condorcet has very
good horizontal responsiveness as well, that is, it is sensitive to subtle
shifts in the median will of the voters along a political spectrum. First,
there is an election with two centrist candidates and two wing candidates
where the slightly further left centrist wins out. Second, the electorate
undergoes a reasonably small overall shift to the right. The result is
that the slightly further right centrist wins the next election.

Here is the sequence:

38: Republican, Right-center, Left-center, Democrat
	(38 total Republican first)
2: Right-center, Republican, Left-center, Democrat
8: Right-center, Left-center, Republican, Democrat
1: Right-center, Left-center, Democrat, Republican
	(11 total Right-center first)
9: Left-center, Right-center, Democrat, Republican
1: Left-center, Democrat, Right-center, Republican
	(10 total Left-center first)
41: Democrat, Left-center, Right-center, Republican
	(41 total Democrat first)

	The Left-center candidate is a clear Condorcet winner in this case. (The
Democrat wins IRV.)

40: Republican, Right-centrist, Left-centrist, Democrat
(40 total Republican first)
1: Right-centrist, Republican, Left-centrist, Democrat
9: Right-centrist, Left-centrist, Republican, Democrat
1: Right-centrist, Left-centrist, Republican, Democrat
(11 total Right-centrist first)
10: Left-centrist, Right-centrist, Democrat, Republican
(10 total Left-centrist first)
39: Democrat, Left-centrist, Right-centrist, Republican
(39 total Democrat first)

	The Right-center is a clear Condorcet winner in this case. (The
Republican wins using IRV.)
	So the point of this, again, is that Condorcet is sensitive to subtle
changes in the electorate along a political spectrum. 
	In this particular example, IRV is sensitive to the same change, but
instead of a correspondingly subtle change in representation, there is a
fairly dramatic change -- what I'd call an over-reaction. Anyway, I'd say
that those are both forms of imprecision: under-reaction and
over-reaction. It is also extremely easy to find examples of IRV or
plurality under-reacting (that is, not responding at all) to a change in
the electorate or to imbalances between the electorate and its
	Actually, my next example is somewhere along those lines. This sequence
departs from the semi-arbitrary ideas of vertical and horizontal
responsiveness, to show responsiveness along multiple dimensions at once.
What is great about Condorcet is that it doesn't just produce a candidate
who is median / majority on one (necessarily oversimplified) overall
spectrum. Theoretically, it tends toward candidates who are median /
majority on several independent issues.
	My example consists of two sequential imaginary races for the
governorship of Ohio. I imagine that the majority favors conservative
economic policies, cultural policies, etc., and therefore votes
Republican. However, I also imagine for the sake of argument that a
majority of the electorate would be open to stricter animal rights laws to
ease the cruel conditions in factory farms (of which there are many in
	In my example, the first Republican candidate is called Taft. Taft has
conservative economic and cultural stances, and also is not in favor of
stricter animal rights laws. 
	The Democratic candidate in my example is called Hagan. He supports
semi-liberal economic and cultural policies. Hagan, if you'd like, would
also be in favor of stricter animal rights laws.
	A third candidate, called Mercer, is a Republican, and supports
conservative economic and cultural policies. However, he is a proponent of
serious animal rights laws.

55: Taft
45: Hagan

	Taft wins the first race, in which Mercer is not a candidate. Although
some of the 55 Republican voters prefer stronger animal rights laws, it is
not worth it for them to sacrifice the other conservative platforms. 

35: Taft, Mercer, Hagan
	(35 total Taft first)
20: Mercer, Taft, Hagan
	(20 total Mercer first)
35: Hagan, Mercer, Taft
10: Hagan, Taft, Mercer
	(45 total Hagan first)

	In this example, the 55 Republican voters all still rank both Republicans
over the Democratic candidate. However, most of the Democratic voters rank
Hagan above Taft because of his animal rights stance. 
	Mercer is a clear Condorcet winner.
	Under IRV, however, Taft would win once again.
	Under plurality, realistically speaking, Taft would win. That is, either
there would be a Republican primary, in which Taft would win and go on to
beat Hagan in the general election, or, if Mercer ran in the general
election, the 20 Mercer voters would most likely vote Taft, for fear of
losing out to the socially more liberal Hagan.
	Under approval, Mercer might have a decent shot at winning. It depends
how many of the Hagan voters would be willing to give up the Democratic
cause for lost, and Approve Mercer as well as Hagan. That is hard to
predict, but again, Mercer does have a shot.

	Here is the point I am trying to make: The median / majority voters' will
on economic and cultural policy is: conservativism. However, the median /
majority on animal rights laws is: yes to animal rights laws. The
candidate who agrees with both medians is selected. I believe that this
kind of example can work with several issue-dimensions rather than only
two. (I will spare you the further examples on this, though.)
	This is an amazingly good property for an election method to have! 
	At best, it means that politicians cannot carry on generally unpopular
policies by politically packaging them in with other policies that the
voters value! It means that a political office has to be responsive along
multiple dimensions at once, rather than just carrying the majority or
plurality of a general spectrum.
	For this reason, it is my hope that with the advent of more sophisticated
election methods such as Condorcet and Condorcet-STV blends, the power and
relevance of political parties as such will decrease, and the power of
voters will increase. That is, the specific views or qualities of a
candidate will become more important relevant to the general platforms of
any party. Even assuming that politicians still group themselves into
parties, I imagine that there will be more room for diversity within

	In conclusion, the point of all this is that Condorcet doesn't lend
itself to stagnation. Quite the opposite! The reason I like Condorcet so
much is that it is by far the most fluid and accurate single winner system
I know of. It is the one which gives the electorate the *most* control
over the politicians. So, no, it is not likely that anyone would become
unassailable under Condorcet. A politician in a sought-after seat has to
either very closely represent the composite median / majority will of the
voters (which is dynamic), or s/he will stand a good chance of being
ousted by someone who does. Either way, Democracy is being served, and
government is maximally responsive to the will of the people.

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