[EM] Paradoxes in Proportional Representation.

[Kristofer Munsterhjelm]

David L Wetzell wrote:
> This is based on what I've culled from empirical findings reported in 
> "Choosing an Electoral System".   
> <http://anewkindofparty.blogspot.com/2011/04/choosing-electoral-system-part-i.html>
> 
> 1. While all forms of PR fall short of proportionality in 
> representation, the best predictor of proportionality is the number of 
> contested seats.  

Only if there are enough parties to provide competition within all the 
seats. If you consider a district that has 20% leftist voters (for 
instance), if there's only one left party, then 20% of the seats (up to 
rounding) will tend to be held by the leftist party. Not very contested; 
and even if you get multiple leftist parties, these will not affect the 
extent to which the right-wing seats (say) are contested.

Rounding may also amplify the apparent contested nature of the seats. 
Say that a district has only two viable parties, and they're even - 
49%-51% of support for each party. Then if you have single-member 
districts, in times of 55% support for the first party, most of the 
seats will go to the first party, and in times of 55% support for the 
second party, most of the seats will go to the second party. Thus all 
seats appear to be contested. Yet, with PR, each would get about half of 
the seats, and some marginal seats would shift back and forth. That 
would seem less competitive, but nothing about the popular support for 
each party has changed: only how the seats are allocated has been.

> Yet, PR with fewer seats induces more turnout than PR with a greater
> numbers of seats. So the election rule that gives us proportionality
> tends to make it so there are fewer competitive seats and less
> uncertainty about election outcomes and consequently lower voter
> participation.

The Hix-Johnston-MacLean document states that these effects are weak. To 
quote:

"Turnout is usually higher at elections in countries with PR than in 
countries without, It also tends to be even higher in PR systems with 
smaller multi-member constituencies, and also tends to be higher where 
citizens can express preferential votes between individual politicians 
from the same political party rather than simply choosing between 
pre-ordered party lists. In general, the more choice electors are 
offered, the greater the likelihood that they will turn out and exercise 
it. However these effects are not particularly strong, there is some 
evidence that highly complex electoral systems suppress turnout, and 
turnout levels may partly reflect influences other than the electoral 
system, for instance in some countries voting is compulsory."

So I don't think you can necessarily draw that conclusion. The apparent 
competitiveness between seats may be lesser (because of what I mentioned 
above in that single-member districts are much more win-all/lose-all), 
but that doesn't mean the real change in voter opinion from term to term 
is any greater in SMD countries.

> 2. Proportionality in representation does not entail proportionality in 
> power and the latter is desired more than the former. As such, it seems 
> that minority dissenters will need to use extra-political methods (not 
> unlike #OWS) to move the center, regardless of whether PR or another 
> mixed system is used.

Proportionality in representation is correlated with proportionality in 
power. The correlation isn't perfect, as Banzhaf and Shapley-Shubik's 
measures make apparent, but to leap on that and conclude that 
proportionality isn't proportional... that's unwarranted.

If anything, when proportional representation disagrees with 
proportionality in power, the power favors the minority parties. Minor 
party kingmakers can make themselves costly if they know there won't be 
any coalition without them. Hence the presence of thresholds in most PR 
systems: these keep too minor parties from becoming potential kingmakers.

Over here, the threshold of 4% keeps most "swing parties" (as one may 
call them) out of power. Yet the threshold is soft - even parties below 
4% of the total vote can get representatives, they just don't get 
MMP-esque compensation on the national level. (Our PR system is a bit 
unusual in this respect: parties get additional seats if their 
per-region seats reflect their national share of the vote too badly.) 
Perhaps you'd want a hard threshold for a less homogenous country, but 
my point is that the problem can be managed.

> 3. If both PR and single-seat elections are in use and the latter favors 
> bigger parties then does PR need to be perfectly proportional or could 
> it be biased somewhat in favor of smaller parties?  Might not the 
> opposing biases tend to cancel each other out?

That's somewhat the idea of MMP. In MMP you have a local election rule 
and a PR rule. Usually the local election rule is Plurality and the PR 
rule is party list, but you could use any combination. Schulze has 
suggested using Schulze STV for a "deluxe" form of MMP - see 
http://home.versanet.de/~chris1-schulze/schulze4.pdf for more about that.

So, yes, if you use both single-seat and PR in the same country without 
  linking the two in some manner, the bigger parties will tend to 
acquire a disproportionate share of the seats when seats elected by both 
methods are considered as one group. To fix this, you can add feedback 
between the types (MMP), or just accept the disproportionality (parallel 
voting).

> These seem to imply that we need not strive for proportionality in 
> representation as the gold standard for electoral reform.  If the two 
> major parties, with a somewhat disproportionate amount of 
> representation, are more dynamic then they'd tend to represent well the 
> majority of the population and heed minorities that frame their issues 
> respectfully. 

Do note, though, that the same Lijphart as you referenced on your page, 
said:

"If partisan conflict is multidimensional, a two-party system must be 
regarded as an electoral straitjacket that can hardly be regarded as 
democratically superior to a multiparty system reflecting all the major 
issue dimensions." ("Democracies: Patterns of Majoritarian and Consensus 
Government in Twenty-One Countries", 1984, page 114.)