Tag Archives: electoral systems

Swing models

Bernie Grofman and I have submitted a paper on what I feel is a fundamental methodological issue in the study of electoral systems, namely how to infer district-level vote changes given national-level vote changes. This has direct relevance to election forecasting and study of partisan gerrymandering, for example. We show that uniform swing and proportional swing, by far the most commonly used methods, fail various natural axioms, and we give an alternative method that does satisfy the axioms. Interestingly, we show that on real data there is very little difference between the predictions made by these methods.

Research news

A few papers are working their way through the journal system:

Once all these are finally done, I can get back to some work on generating functions, after several years, which I am very much looking forward to.

 

Multi-district preference modelling

This paper with longtime coauthor Geoffrey Pritchard is an important step toward systematic design of electoral systems.

Abstract: Generating realistic artificial preference distributions is an important part of
any simulation analysis of electoral systems. While this has been discussed in some de-
tail in the context of a single electoral district, many electoral systems of interest are based
on districts. Neither treating preferences between districts as independent nor ignoring
the district structure yields satisfactory results. We present a model based on an extension
of the classic Eggenberger-Pólya urn, in which each district is represented by an urn and
there is correlation between urns. We show in detail that this procedure has a small num-
ber of tunable parameters, is computationally efficient, and produces “realistic-looking”
distributions. We intend to use it in further studies of electoral systems.

2011 referendum simulator: experience so far

Several months ago I realized that the 2011 referendum in NZ on the voting system for parliamentary elections was coming soon. Geoff Pritchard and I developed a simulator with the aim of enabling voters to understand the consequences of a change to another system. In order to do this in a way that is useful to the non-expert, some simplifying assumptions must be made. We had substantial media coverage and some criticism.

Initial surprises:

  • How few people bothered to read the detailed FAQ before criticizing.
  • How many people thought that the simulator was trying to “back-cast” historical elections, and were certain that our results were unrealistic, without giving any evidence.
  • How much the criticisms, even unfounded ones, helped to clarify my understanding of what we had actually done, and suggested further research.
  • How short the attention span of internet visitors is.

In particular I want to respond to comments by David Farrar on his well-known site Kiwiblog. The relevant extract:

Now in 2002 National actually won 21 electorate seats out of 69 or 70. So this model is saying if there were 50 extra electorate seats, National would win 11 fewer seats!!

Why? Because they have come up with a formula based on the last 50 years or so of FPP elections, which they applied to the party vote figures for 2002. They ignored the actual electorate vote. It is a classic academic approach.

The more pragmatic approach, which is what others have done, is to say well if National won 21 electorate seats in 2002 out of 70, then if there 120 seats, their estimated number of seats would be 21*120/70, which is 36 seats.

In fact we did not look at any of the historical FPP elections The “formula” is based completely on the MMP party vote from the 2008 election (so yes, we did ignore the electorate vote, for what we think are good reasons).

However this got me thinking about how we might try to validate our assumptions. One way which I don’t (yet) claim is rigorous, but makes at least as much sense as the above, is to apply the simulator (the FPP part) to the historical FPP elections, and scale the 120 seats down to whatever it was historically (80 for many years, then increasing over time). The results surprised me greatly, as they are much better than expected, and this cries out for explanation (“further research”, always good for academics). Here they are. Note that these simulator results explicitly do not use any historical data, seat boundaries and parties have changed, etc.

1969: Real result was Nat 45 Lab 39; simulator scaled was Nat 46.9, Lab 37.1
1972: Real was Nat 55 Lab 32; simulator scaled was Nat 54.4, Lab 31.6
1975: Real was Nat 55 Lab 32; simulator scaled was Nat 55.1, Lab 31.9
1978: Real was Nat 51  Lab 40 SoCred 1; simulator scaled was Nat  47.5, Lab 44.5.
1981: Real was Nat 47 Lab 43 SoCred 2; simulator scaled was Nat 48.3, Lab 43.7
1984: Real was Nat 37 Lab 56 SoCred 2; simulator scaled was Nat 37 Lab 58.
1987: Real was Lab 57, Nat 40; simulator scaled was Lab 50.2, Nat 46.8
1990: Real was  Nat 67, Lab 29, NewLab 1; simulator scaled was Nat 71, Lab 26
1993: Real was Nat 50, Lab 45,  NZF 2, Alliance 2; simulator scaled was Nat 53.6, Lab 45.4