Category Archives: Electoral Reform & Senate Reform

Dynamics of the Alternative Vote

It’s incredibly difficult to assess the impact of an electoral reform ex ante. The problem is that parties’ and voters’ strategies are endogenous to the electoral system.  This is one reason why the analysis of electoral reform so often has to operate on the basis of first principles. However, given the vagaries of social choice theory (generally no equilibrium for 3+ options in 2+ issue dimensions), there are limits to what we can say on the basis of first principles. For this reason, it’s still useful (and interesting) to look at data to learn about the impact of electoral reform.

The Spaniel is on record as preferring a “ranked ballot” electoral system – or the “Alternative Vote” (AV) as the system is known in Australia, where it has long been used at federal and state elections.[1]  With their majority, the Liberals can impose an AV on the country – and, as I have argued previously, they have strong incentives to do so. Theoretically, AV works to the advantage of large, centrist parties like the Liberals. Correspondingly, it (theoretically) works to the disadvantage of both smaller parties and identifiably left- or right-wing parties; the former are disadvantaged by AV’s use of single-member districts; the latter, by the fact that they are less likely to be the second-preference of many voters.

Given that, it is interesting to look at how AV has worked out Australia, how the transition from FPTP to AV in Australia altered the effective number of parties that contested elections and won seats, the proportionality between votes & seats, the support for third-parties, and the level of electoral volatility. (Keep in mind that electoral reform was itself often undertaken by incumbent government’s in response to a threatening change in the party system, e.g., a growing Labor party.)

The Australian experience with AV is quite unique; I know of no other major country that has had such long experience with AV.  But that makes it problematic to draw inferences about how AV might affect Canadian politics: we can’t know which aspects of Australian electoral and party competition are due to the inherent dynamics of AV and which are due to Australia being, well, Australia.  To get around this (but, to be honest, only part way around this), I examine elections in Australia’s five mainland states as well as in the Commonwealth.[2]  To the extent that trends are common across all 5 states and the Commonwealth, we can assume that that’s due to the (common) electoral system and not the peculiarities of the state.

The Australian state data are especially useful because, like the Commonwealth, the five mainland states used FPTP before adopting AV. This allows one to assess the impact of transitioning from FPTP to AV within each state.  Now, the transition was not always direct as Table 1 below shows: NSW experimented with a two-round plurality system (of the sort used for elections to the French National Assembly), STV, and the Contingent Vote before adopting AV; Queensland only adopted AV in 1963.[3]  In addition, FPTP was not always employed with single-member districts. South Australia applied both the plurality rule and the alternative vote in 2- and 3-seat districts.


Table 1.  Electoral Systems used in Australia, 1890-2015



























The Effective Number of Parties

One of the first things a political scientist likes to know about a country is how many parties contest elections and win seats.  The longstanding notion is that the number of parties is closely related to political stability, the potential for polarization, and the capacity of electoral politics to represent diverse interests. Now, not every party counts as interesting or relevant; for example, we probably want to discount fringe parties that obtain .5% of the vote — but arbitrarily ignoring some parties (which ones?) is problematic.  Consequently, political scientists tend to focus on the effective number of parties (Laakso & Taagepera 1979).  We either count the effective number of electoral parties (i.e., the number that contest elections) and/or the effective number of legislative parties (i.e., the number that win parliamentary seats).  We obtain the effective number of electoral parties by constructing a Herfindahl-Hirschman Index (HHI) of parties’ vote shares, with vote shares expressed as proportions.  Similarly, we obtain the effective number of legislative parties by constructing a HHI of parties’ seat shares, with seat shares expressed as proportions.  (The difference between the two statistics can be informative.  For example, we often see large deficits in the number of parties that contest elections and win seats in transitional democracies where expectations about parties’ competitiveness have not yet congealed.)

The Effective Number of Parties in Australia, 1890-2015

Figure 1 shows the effective number of electoral and legislative parties in the Australian Commonwealth and the five mainland states over time. These statistics provide a rough means to track the relationship between the electoral system and the party system. For example, we can use the data in Figure 1 to assess if changes to the electoral system precede sharp changes in in the number of parties that contest elections or win seats.


Australia: ENEP & ENLP by State

(Click on the figure to enlarge it)

From a theoretical perspective, one would not expect a shift from FPTP to AV to have a big impact on the effective number of parties. This is because both systems tend to be used in conjunction with single-member districts (i.e., districts magnitude = 1), and theory (Cox 1997) predicts M + 1 effective parties to contest elections. (And, because parties are unlikely to persist in contesting elections unless win at least some seats, to secure legislative representation, we might also predict M+1 legislative parties). The prediction is a weak one, however, because Cox’s M+1 rule operates at the district-level – and different sets of M + 1 parties could present themselves in different districts. Still, the dashed line in each panel of Figure 1 shows this M+1 threshold for each state.

Between 1940 and 1980, South Australia’s party system closely adhered to this theoretical prediction, with just 2.5 effective electoral parties and 2.25 effective legislative parties. However, the main message of Figure 1 is that the effective number of electoral and legislative parties can and does wander from this M+1 equilibrium. Observe, for example, the growth in the number of electoral parties in the post-1980 period at both state and federal levels. Plainly this post-1980 increase in electoral parties is not due to the main features of the electoral system because by this point in time all mainland state and federal elections in Australia were held under AV.

In addition, the effective number of electoral and legislative parties was pretty much the same under FPTP and AV controlling for differences in district magnitude. The effective number of electoral parties in each state and federally averaged about 3 (i.e., M + 2), and the effective number of legislative parties in averaged about 2.5 — and did so under both FPTP and AV.

Nor is there any evidence that changing the electoral formula from plurality to AV leads to changes in the effective number of electoral or legislative parties. Indeed, the evidence on this front is far more consistent with Cox’s view that it is mainly the district magnitude that shapes party competition. To show this, I ran regressions of year-to-year changes (i.e., first-differences) in the effective number of electoral (ΔENEP) and legislative parties (ΔENLP) on contemporaneous and lagged changes in the electoral formula (ΔF, ΔFt-1) and district magnitude (ΔM, ΔMt-1):

ΔENEPst = a + b1ΔFst + b2ΔFst-1 + b3ΔMst + b4ΔMst-1 + ust (1)

ΔENLPst = a + d1ΔFst + d2ΔFst-1 + d3ΔMst + d4ΔMst-1 + est (2)

The results (below) indicate that 1) an increase in the district magnitude in year t increases the number of electoral parties by .34 in t and the number of legislative parties by .21 in t+1.[4]

Table 2. OLS Model of Changes in the Effective Number of Electoral and Legislative parties

The Effective Number of Parties in Australia, 1890-2015




.29 (.15)

.14 (.17)


.23 (.23)

.03 (.08)


.34*** (.07)

.09 (.13)


.10 (.26)

.21*** (.05)


.005 (.01)

.01 (.006)

N Obs



R2 = .04



Robust SE clustered by state in parentheses


What these data suggest is that the introduction of AV in Canada is unlikely to generate major changes in the effective number of parties that contest elections or win seats. Canadian federal elections from 1949-2015 have been contested by 3.3 effective electoral parties, and produced an average of 2.5 electoral parties (not far off the Australian figures). The adoption of AV can be expected to leave these statistics intact precisely because such a reform would leave the district magnitude intact. This does not, of course, rule out changes in the identity of parties that contest elections or win seats or the possibility of major shifts in vote- or seat-shares between parties (because the effective number of parties remains the same whether the Liberals gain 35% of the vote, and the NDP, 15%, or the converse.)

In the next post, I’ll consider if/how the transition from FPTP to AV in Australia altered votes-seats proportionality.


[1]  Under AV, voters (typically in single-member districts) rank their preferred candidates from 1-N. If any candidate secures 50+% of voters’ first-preferences, s/he is declared elected. If not, the lowest ranked candidate is eliminated and ballots cast for the eliminated candidate are distributed to the remaining candidates according to second-preferences. If any candidate secures 50+% of voters’ first- and second-preferences, s/he is declared elected. If not, the lowest ranked candidate is again eliminated and ballots redistributed, etc.

[2] Many thanks to my colleague, Campbell Sharman, for furnishing me all these data on Australian elections.

[3]  The contingent vote (CV) is a hybrid between FPTP and AV: Under CV, the voter lists up to two preferences on their ballot, one for the most-preferred candidate and a second-preference for another candidate. If there is no majority-winner on first-preferences, then all candidates but the top-two are eliminated, and ballots cast for those candidates are redistributed according to second preferences. The winner is then the candidate with the plurality of first- and second-preferences.

[4]  Using first-differences obviates the need to include state fixed-effects. Now, the model does restrict the coefficients to be the same across states, but there’s not really enough variation to allow for the coefficients to vary by state.  Also, it’s clear that changes in formula include shifts from say, STV to CV, as in NSW; they are not just confined to transitions from FPTP to AV. But the results are largely unaffected by, say, dropping NSW from the model.


Right after the election, the rumbling for electoral reform began.  The impetus was 1) the Liberals’ manufactured majority, and 2) their promise to replace Canada’s electoral system from First-Past-the-Post to … well, something else.  I wrote a blog post noting … Continue reading


The NDP clearly hope to use the Liberals’ promise to effect electoral reform to replace FPTP with a mixed-member proprtional system (MMP). This is precisely what the NDP promised in its election platform (, and it is why the NDP … Continue reading


An aside before today’s main post:  I hear a lot of commentators describing what the Liberals are trying to effect as “democratic reform”.  That’s not quite so: the Liberals are trying to effect electoral reform.  The phrase “democratic reform” is … Continue reading

Some jumbled thoughts on the strategy of electoral reform

I posted yesterday of my plan to write several blog post on the Liberals’ plans for electoral reform and Senate reform. My focus is going to be on the strategic and tactical aspects of the government’s initiatives in these areas, and on how we might expect the opposition parties to react. I’ll start today by discussing electoral reform.  I am having trouble developing a coherent model of the politics of electoral reform, and so I’ll content myself by posting a series of rambling observations.

What the Liberals probably want to achieve

While the vague nature of the Liberals’ promise to reform the electoral system theoretically allows them to choose among a wide variety of alternative electoral systems, their choice is essentially over three three key aspects of the electoral system: 1) the district magnitude (i.e., the number of seats available in the district), 2) formula (i.e., plurality, majority, or PR), and 3) ballot structure (preferential or simple). The general effect of altering each of these dimensions is as follows:

  • The larger the district magnitude, the more political parties one can expect to contest elections and win seats. Specifically, if we denote the district magnitude as M, we can expect M+1 parties to contest elections (Cox 1997).
  • Proportional representation facilitates the electoral success of smaller parties, especially ones with with well-defined ideological niches. The propensity of PR to favour smaller parties is contingent on the district magnitude, however. The lower the district magnitude, the less proportional the translation from votes to seats, and the less “friendly” the electoral system is to smaller parties.
  • A preferential ballot structure favours centrist parties (and their candidates) because they can reasonably expect to be the second preference of many voters who prefer the more extreme parties to the left and right.

We can safely assume that the Liberals prefer to replace FPTP with an electoral system that reliably provides them with 1) at least a plurality of parliamentary seats such that they 2) regularly participate in government. To achieve this, the Liberals must choose an electoral system that simultaneously 1) prevents the Conservatives from capitalizing on the divisions between the Liberals, NDP, and the Greens and yet 2) still ensures that the Liberals are the dominant left-wing party.

List-PR, especially in large multi-member districts, is unlikely to achieve these ends. As a larger party, the Liberals benefit from electoral disproportionality. The risk inherent in adopting a highly proportional electoral system—such as list-PR in large multi-member districts— is thus that it would reduce the Liberals to just one of three fairly co-equal left-wing parties.* If this happened, the Conservatives might be able to form minority governments on a regular basis in a mirror image of the historical Swedish pattern, where a lack of coordination among three right-wing opponents often allows the left-wing Social Democrats to form single-party minority governments. This line of analysis suggests that the Liberals prefer to keep the district magnitude low. In this respect, the Liberals’ interests dovetail with those of the Conservatives, the other large party, and clash with those of the Greens and the NDP.

It’s unlikely, of course, that the Liberals would champion list-PR as the alternative to FPTP. Instead, they are likely to take their cue from recent electoral reform efforts in Ontario and BC, where voters were asked to consider replacing FPTP with mixed-member proportional representation (MMP) or the single-transferable vote (STV), respectively.  Both MMP and STV would do a better job than list-PR of protecting the Liberals’ position as the dominant left-wing party in Canadian politics. Under MMP, the Liberals could confidently predict to win large pluralities of district seats. This would leave them as obvious formateurs of any left-wing coalition government. STV could be applied in multi-member districts of, say, 3 seats. This would generate sufficient disproportionality to ensure that NDP and Greens could not eclipse the Liberals as the dominant left-wing party. In addition, the Liberals could expect to be the main beneficiary of NDP and Green voters’ second preferences.

Constraints / Why I think the Liberals are unlikely to opt for MMP (especially) or STV

The main problem with STV and MMP (especially) is feasibility. Both STV and MMP would require effecting a country-wide redistribution of riding boundaries. This would be hard to do given the Liberal’s self-imposed time frame of 18 months to introduce the necessary legislation. (Presumably that legislation will have to include district boundaries.  Of course, given their penchant for setting arbitrary deadlines, and then screwing the pooch in an effort to meet said deadlines, the Liberals might not give a damn about rushing through a country-wide redistribution – damn the torpedoes – before the next election.)

Such considerations leave STV as a dark horse alternative IMO, but they do not make it a non-starter.  The problems confronting MMP run much deeper, however. MMP is likely to find itself in tension with the “senatorial floor” clause in of the 1867 Constitution Act. This clause guarantees each province at least as many seats in the House of Commons as it has in the Senate. The need to respect the senatorial floor clause will in my view mandate that any MMP system operate on a provincial rather than a national or regional basis, unless the Liberals are willing to substantially increase the size of the House to accommodate the list-tier seats (and this is probably a non-starter).**  The huge variation in the size of provinces would then generate wide variation in proportionality across provinces.  I could see this as fertile ground for legal challenges.*** While the courts have generally granted Parliament wide latitude in structuring the electoral system, any law suit would eat up limited time.  I just can’t see the Liberals fighting in the House, the media, or the Courts for MMP: MMP just doesn’t give the Liberals’ sufficient electoral return to justify all the potential trouble.

Almost by default, then, the Liberals are left with  the alternative vote (AV) (i.e., ranked ballots) as their most preferred alternative to FPTP. AV has three key advantages from the Liberals’ perspective: 1) it uses single-member districts, so it can be effected without altering existing riding boundaries; 2) precisely because AV uses single-member districts it is disproportional, and as such it tends to operate to the benefit of larger parties (like the Liberals); and 3) AV tends to benefit “moderate” parties, that is, parties that can expect to be voters’ first or second choice. As the centre party of the Canadian party system, the Liberals can reasonably expect to be the second preference of progressive Conservative voters, and also of mildly left-wing voters who are suspicious of handing power to the NDP or the Greens. STV in small districts is almost as advantageous for the same reason.

I don’t think the above is especially earth-shattering, but it does help establish the Liberals’ preference orderings over electoral systems:

AV >> STV (given small M) & FPTP > MMP.

It’s not exactly clear to me how the Liberals value STV relative to FPTP. My thinking is that there’s a district magnitude above which the Liberals prefer FPTP.

In the next few posts, I’ll consider electoral reform from the Conservative and NDP, Green & Bloc perspectives.  This will help to identify potential coalitions for the various alternatives.  I’ll then consider how it all might go pear-shaped for each of the parties.

*Large-M list-PR poses another risk to the, the Liberals and the Conservatives, and that is that it will encourage their fragmentation into smaller, more ideologically coherent parties. Of course, I would expect all parties to champion a closed-list to forestall this possibility and retain their oligopoly on the Canadian party system.

**Consider, for example, that the senatorial floor, for example, constitutionally guarantees PEI 4 seats.  I don’t see how one could, say, amalgamate PEI’s 4 ridings into 2 ridings, and then argue that 2 seats on a national list of 169 seats are somehow PEI’s.  Which 2 seats would those be and what is the electoral connection between the PEI electorate and the occupants of said seats?  I’ll bet that PEI (and every other province) will demand that the electoral connection between the province and its House of Commons’ seats be crystal clear — and I’d bet the SC sees things the same way.  I see two ways to achieve this:
  1. Double the size of the HOC.  PEI would then retain its 4 district seats – and “presto”, problem solved.
  2. Use provincial lists (as in Germany).  This is far more likely.  Of course, it’s less desirable from the perspective of the NDP and the Greens (especially) because smaller lists (especially in Atlantic Canada) will preserve some disproportionality. This will favour the Grits and Tories.

***In Germany, for example, small parties successfully litigated the practice of the larger parties retaining their überhängmandaten; this violated the guaranteed of proportionality, they argued.  I could see similar arguments being made if the Liberals worded the legislation so as to require the electoral system “make every vote count”  (the phrase employed in their platform).  Of course, this problem dogs FPTP due to malapportionment across provinces (also a function of the senatorial floor), and several groups have tried to litigate against FPTP on these grounds.  The difference is that litigants will now be able to ground their challenges on a specific piece of legislation as well as the Charter.