Category Archives: Electoral Reform & Senate Reform

It’s been a long time since I wrote a blog post, but impetus has come in the form of Jenny Kwan’s latest “10-percenter”*. (Kwan – unfortunately for me – is the MP for Vancouver East, where I live.) The 10-percenter is on electoral reform, and specifically on the virtues of PR. That’s both understandable and logical given that Kwan sits for the NDP: the NDP bear the brunt of our SMP system’s disproportionality and would likely see their seat share and policy influence increase under PR. If you are an NDP supporter, you ought to support PR on that basis: it’s in your political interest.

Kwan’s pamphlet doesn’t make that kind of straightforward argument, however. Instead, it offers up a rather incoherent and biased comparison of the current electoral system (single-member plurality) and PR. Here’s the full text of Kwan’s pamphlet; I’ve highlighted areas that I examine in greater detail below:

Defenders of the status-quo will likely tell you that proportional voting systems lead to chaos – with endless elections and instability. But the reality is the exact opposite is true.

Canada already has a lot of federal elections. In fact, we’ve had 22 in total since 1945. That makes us more “unstable” than Italy, a country that uses proportional representation and has had just 18 elections over the same period.

Proportional elections eliminate “false majorities” by ensuring no party gets a higher percentage of seats than their percentage of votes. That forces political parties to work together and deliver results in a stable coalition government.

Beyond making our elections fairer and more stable, proportional systems have many other positive impacts on the countries that use them. For example, they tend to have stronger economies with higher surpluses, lower deficits, and less debt.

Countries where parties work together collaboratively are also more likely to tackle two of the biggest issues of our time: climate change and income inequality.

With consultations on democratic reform underway, we have a once in a lifetime opportunity to build a better Canada with fairer elections. We have to get it right.

Let’s start with the incoherent aspects of this argument. The first claim here – if I follow – is that elections are finite in occurrence under PR; that is the exact opposite of “endless elections” is it not? Speaking as a person who prefers to live in a democracy, let me say that I really hope that elections are endless! I guess the question that Kwan’s constituents should pose to her is when will elections end under PR, after one election or two?

The second puzzling aspect of the argument is the comparison that Kwan draws between politically “unstable” Canada and politically stable Italy. Huh?! It’s not only that the data that Kwan presents on this front are highly misleading (see below), but that Italy is precisely the wrong country to bring up when trying to establish that PR’s does not imply political instability. I could see bringing up Austria or Germany or Sweden…. but Italy??

To see how misleading Kwan’s comparison is one needs to appreciate that the metric of political stability in the electoral systems literature (see, e.g., Powell (1982), Lijphart (1999), Farrell (2001, 193)) is not the frequency of elections but cabinet duration. One good reason for this is that the time between mandated elections varies substantially across countries; it’s just 3 years in Australia, for example. Indeed, if I crack open my Stata and upload a data set on elections and cabinets in OECD countries from 1945 onward I find that Australia’s had 27 elections since 1945. Do you think that Australia’s been the least stable OECD country over the post-war period? Me, neither.

So let’s consider how Canada and Italy perform in terms of cabinet stability over the post-war period. (A caveat here is that my data are not well configured to estimate cabinet longevity because they are formatted by election not by cabinet, and while I am exercised by Kwan’s distortions, I’m not so exercised that I’m going to take 45 minutes to reformat my data set). Bearing that caveat in mind, my data (all publicly available on ParlGov) do allow me to present two metrics of cabinet stability:

1. the average number of cabinets per year, and
2. the average duration of the initial cabinet, i.e., the cabinet first installed after a general election

My data on Canada cover 70 years, from June 1945 – November 2015.

• In that period, Canada was governed by 27 cabinets, for an average of .39 cabinets per year.
• In Canada, initial cabinets (and there’s never been more than 3 in any parliamentary term) have survived an average of 1116 days. This is 61 percent of the maximum time period of 5 years between Canadian elections.

My data on Italy cover 66 years from May 1948 – February 2014.

• In that period, Italy was governed by 62 cabinets, for an average of .94 cabinets per year.
• In Italy, initial cabinets (and Italy’s averaged 3.65 per parliamentary term) have survived an average of 524 days. This is 30 percent of the maximum time period of 5 years between Italian elections.**

The difference here is stark. Italian cabinets have been less than half as durable as Canadian cabinets over the post-war period. Thus Kwan’s claim that Italy has had fewer elections than Canada in this period is true, but it’s also incredibly misleading as to which country’s had the more stable governments. (An irony here is that Kwan’s district includes Vancouver’s traditional Italian neighborhood, and so many of her constituents will know exactly what a political basket-case Italy is.)

Now one can certainly debate whether cabinet durability is an informative normative metric; Lijphart (1999), for example, argues that cabinet durability is not necessarily a good indicator of policy-making effectiveness. And we can have too much durability – ossification – as well as too little. But that’s a different argument.

Let me move on to the old “false majority” chestnut. (This critique of SMP just won’t go away – sigh.) It is true that plurality electoral systems occasionally produce elections in which the 2^nd-place party in terms of vote share wins the plurality of seats. Note that this is a system-level not a district-level phenomenon. In each district, it’s the candidate with most votes who wins. However, a party’s vote share can be spread in a very inefficient fashion across seats (large majorities in a minority of districts) such that it secures a large vote share but a small seat share. It’s hard – but not impossible – to generate similar distortions under PR; the key is to have a small district magnitude (and many districts) as in Chile’s “binomial” electoral system.

More to the point, PR can easily produce another kind of “false majority”. Imagine that an electorate is comprised of three types of voters with preferences over 3 parties, a, b and c as shown in the table below. Thus voters of Type A prefer party a first, b, second, and c, third. Let’s say that there’s a rough equality between types of voters (so 33% of each), and that they vote sincerely. Thus, parties a, b and c gain roughly equal shares of votes and seats, the electoral system being highly proportional. All parties have equal legislative power under these conditions, and any two can form a majority coalition. Let’s say that a and b form a coalition.

Now, on one hand, a coalition of a and b can claim to enjoy the support of a majority because, 2/3 of voters voted for either a or b. On the other hand, the electorate was not presented with a choice over all possible outcomes; they got to vote only for a or b or c – not a coalition of a & b, b & c, or a & c. If voters had been given such a choice, a majority might well have voted for a coalition of a & c given that all a-types prefer a and a & c to b and all c-types prefer c and c & a to b. On this basis, one could argue that the coalition of a and b reflects a “false majority”.

There are two points here:

1. “False majorities” do not disappear under PR; they just take on a different and less obvious form; these “false majorities’ are not at all inevitable, but they cannot be ruled out ex ante;
2. Using the concept of a “false majority” to evaluate an electoral system is a dead-end.

I can expand on the second point: One of the central messages of social choice theory is that it’s almost never possible to identify if there exists a coherent and uncontradicted majority in favour of a particular policy or outcome (save in the case of a majority vote over two alternatives). The problem (as I have written and spoken about again… and again… and again) is that the electorate is better understood as an agglomeration of multiple, partly conflicting majorities. The idea is pretty simple: sure, there may exist a majority for policy X and also one for policy Y – but it does not follow that there necessarily exists a majority in favour of both X and Y.

The rest of the claim is no better. The statement that proportional representation “ensur[es] no party gets a higher percentage of seats than their percentage of votes” is not wholly accurate. As Douglas Rae (1967, 134) observed “The prejudice of electoral laws – and here I include even the P.R. systems (my emphasis) – in favor of strong elective parties and against weak ones is very nearly a universal fact of life.”(By strong parties, Rae meant those polling more than 20 percent.)

The reason this occurs is due to a variety of factors; the two main ones are a finite, and typically quite low district magnitude in most electoral systems, and electoral thresholds. If the district magnitude is below 5 or 6 and the electoral threshold in the neighborhood of 5 percent, it’s quite possible for a PR system to deviate significantly from proportionality – and this deviation always favours larger parties. (Certain quotas – like the Imperiali quota — also systematically favour larger parties.)

The last part of the claim, that proportionality “forces political parties to work together and deliver results in a stable coalition government” is not so much false as it is contingent. Certainly, cooperative, stable coalition government is one possible outcome of a PR electoral system; that’s largely the German, Austrian, and Dutch experience.Two other alternative outcomes are possible and widely observed, however.

The first alternative is what Giovanni Sartori (1976) termed polarized pluralism: a pattern of party fragmentation, unstable coalition governments, and policy immobility. This is the French 4^th Republic, Italian, Belgian and Israeli experience. The second alternative is minority government; this is Swedish, Norwegian and Danish experience (see Strom 1990).

I actually think this second alternative is the most likely outcome in the Canadian case were we to adopt PR. The fact that Canadian opposition parties have allowed minority governments to form and last indicates that there are significant (unobserved) costs to joining a government and/or bringing down a government in Canada, and possibly significant (unobserved) benefits to being in opposition; else opposition parties would have forced our minority governments into coalition or brought them down immediately. In addition, the structure of the party system facilitates minority government. Let’s say that the Liberals get a plurality of seats under PR and the NDP says “let’s make a coalition.” The Liberals can tell the NDP (and Greens) to go pound sand. What are the NDP going to do? Bring down the Liberals in favour of the Tories or a new election? PR may deliver different seat shares to the smaller parties, but unless the configuration of the party system also changes substantially, it will not necessarily increase their legislative power.

Moving on to our unfair and unstable elections… (Are Canadian elections unstable, marked by widespread violence and irregularities? Perhaps in the 1870s…. but nowadays?) The claim here is that countries that use PR have “stronger economies with higher surpluses, lower deficits, and less debt.”

I am not sure where Kwan gets the statistics to back this statement up because the debate on the macroeconomic effects of electoral systems is far from settled. Lijphart (1999) made similar statements about the superiority of consensus democracies (which use PR) in Chs. 15 and 16 of “Patterns of Democracy”, and in his 1997 EJPR piece he declared: “the results of statistical analysis were clear and almost completely unequivocal. . . Over-all, consensus democracy is superior to majoritarian democracy. I have no second thoughts about these conclusions.”

Lijphart’s evidence was not particularly strong, however; it consisted mainly of a series of bivariate regressions on data up to the 1980s. When Anderson (2001) re-analyzed these data he found that the superior macro-economic performance of consensus democracies disappeared once one controlled for corporatism and central bank independence. In fact, controlling for these two factors (which are not themselves due to the electoral system), Anderson found that consensus democracies had higher rates of inflation and unemployment than majoritarian democracies. These results are consistent with work by Rogowski and Kayser (2002) that finds that price levels are higher in PR systems. Related work by Bawn and Rosenbluth (2006) finds that government spending grows in line with the number of parties in government. That said, Iversen and Soskice find systematically less economic inequality under PR.

The reality is that one could line up literature on both sides of the claim that PR is good / bad for the economy.  My own view is that the electoral system probably has only a small effect on economic outcomes. Other, more fundamental institutions – the rule of law, constitutional limitations on government – probably have a greater impact in the sense that for a society that gets these fundamentals right the electoral system probably doesn’t really matter much. Conversely, get these fundamentals wrong, and changing the electoral system is unlikely to make a damn bit of difference.

* A “10-percenter” is a newsletter that an MP can send to 10% of her constituents on the federal government’s dime.

**OK, so these are not median survival times from a well-specified Cox Proportional Hazards model, and as such they may suffer from right-censoring.  BUT 1) any right-censoring probably understates just how much more stable Canadian cabinets have been relative to Italian cabinets, and 2) this blog is not intended to be a statistics symposium, in any case.

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The final exam for my Strategy & Politics class always takes the same form:  I ask my students to apply what they have learned about game theory and parliamentary history to make sense of a contemporary political controversy.  The topic of this year’s exam was the partisan machinations around the Canadian Senate, that is, 1) the Conservatives’ threat to deploy their (temporary) Senate majority against the government’s legislative program, and 2) the Liberals’ promise to reform the Senate by installing non-partisan Senators via a “merit-based” selection process.  Will the Conservatives’ erect a Senate roadblock, and will the Liberals then break their promise and stack the Senate with Liberal hacks?  Or are both sides more likely to compromise, with the Conservatives passing duly diluted Liberal legislation through the Senate?

I always write up a template answer to the Strategy & Politics final exam that I give my students, and with the House’s attention now on Senate Reform, here’s my answer to my own question:

The Conservatives have threatened to use their Senate majority to stall the Liberals’ legislative program. (OK – they have toned down this kind of talk recently.) The Senate has the constitutional power to veto all legislation save that which is financial in nature. Furthermore, the Conservatives enjoy a majority in the Senate. To that extent the Conservatives’ threat is not an idle one. However, as Table 1 below shows, there are 22 vacancies in the Senate. Were Prime Minister Trudeau to fill these vacancies with loyal Liberals, the Conservative majority would vanish. But the Prime Minister has promised not to do this; instead, he proposes to appoint Senators on the basis of merit as recommended by a non-partisan board. Adding to the complexity of the situation is the fact that while in opposition Trudeau expelled Liberal Senators from the Liberal caucus. This implies that Liberal Senators are not bound by party discipline. Common ideological preferences may well lead many Liberal Senators to vote the party line, but it cannot be guaranteed.

Table 1. Party Standings in the Senate

I consider 3 questions in light of this situation: 1) How can the Conservatives be expected to deploy their Senate majority? 2) How is the Government’s proposal likely to alter the situation? 3) Are the Liberals likely to follow through on their merit-based appointment process?

1. How can the Conservatives be expected to deploy their Senate majority?

I use a a spatial model the parliamentary situation to understand how the Conservatives can be expected to deploy their Senate majority. Figure 1 depicts the distribution of parties along the left-right spectrum in both the House and the Senate. I assume that the parties are all perfectly cohesive (so a single ideal point suffices to represent the preferences of party members), and that parties’ respective positions are identical across the House and Senate. I also assume that the 9 independent Senators share an ideal point midway between the Liberals and the Conservatives; this will be a useful simplification. Actors have Euclidean preferences.

The Liberals enjoy a majority in the 338-seat House of Commons, and hence the median voter in the House is a Liberal MP; measures pass the House only with the support of this Liberal MP (i.e., the House median). Similarly, the median voter in the Senate is a Conservative; measures pass the Senate only with the support of this Senator (i.e., the Senate median). Policies in between the House and Senate medians cannot be moved. To appreciate this, consider the status quo policy, SQ, in this interval: if the Liberals try to replace SQ by an policy at their own ideal point, the Conservatives can use their Senate majority to veto the move; the policy will therefore remain at SQ.

The Conservatives cannot arbitrarily exercise their Senate veto. The Senate is an unelected body, and as such it lacks legitimacy among the Canadian electorate. To use it to veto every Liberal bill would allow the Liberals both to paint the Conservatives as obstructionist and to build a case to bypass the Senate (e.g., by abolition). I model this by assuming the Conservatives pay a cost, c > 0, for exercising their Senate veto. This cost creates an “envelope” of ±c around any status quo policy within which the Liberals have discretion. For example, were the Liberals to replace SQ by any point between SQ-c and SQ, the Conservative would allow it to pass because the cost of vetoing any such policy would exceed the gain associated with keeping policy at SQ.

The model highlights that the parliamentary situation is defined by a key relationship between two variables, the ideological distance between the Liberals and Conservatives, |LIB-CON|, and 2) c, the cost to the Conservatives for exercising their Senate veto. In particular, the Conservatives’ incentive to veto Liberal bills is strong only if they perceive the cost of deploying their veto to be small relative to the distance between their ideal point and the Liberals’, i.e., c << |LIB – CON|. Under opposite conditions, (i.e., c >> |LIB – CON|), the Conservatives would rarely have an incentive to use their Senate veto.

2. How is the Government’s proposal likely to alter the situation?

The reasoning above identifies conditions under which the Government’s proposal to appoint Senators on merit rather than partisanship is moot, i.e., c >> |LIB – CON|. The interesting case is one in which the Liberals’ and Conservatives’ positions are far apart, and Conservatives perceive the cost of a veto as quite small. Let’s assume that these more interesting conditions obtain.

Even so, how the Government’s proposed appointment process is likely to alter the parliamentary situation depends critically on the ideological distribution of meritorious individuals. Consider two reasonable possibilities: 1) that meritorious individuals are as likely to be left-wing as right-wing, or 2) that meritorious individuals are – in Canada, at least – likely to be left-of-centre in their ideology. These two situations are depicted in the top and bottom panels of Figure 2, respectively. The bell-curves in the panels reflect the (normal) ideological distribution of meritorious individuals, the set of people from which a putatively non-partisan board would select Senate appointees. For simplicity, the distance between the Liberals and Conservatives is scaled to be two standard deviations of this same ideological distribution.

Figure 2. Possible ideological distribution of meritorious individuals

What would be the effect of 22 non-partisan appointments were the ideological predisposition of those appointees as depicted in the top panel of Figure 2? Under such conditions one would expect approximately 3.5 appointees would hold positions to the Conservatives’ right.¹ The Conservatives’ could expect the regular support of such individuals. Another 7.5 appointees could be expected to hold positions between the ideological centre (at 0) and the Conservatives’ position. The Conservatives would require the support of just 3 to 4 of these individuals to maintain a majority. The Senate median would therefore shift to the left under these conditions, but not by much; it would fall about midway between 0 and 1.² Furthermore, the occasional defection of even 1 or 2 Liberal Senators (who, recall, are not under party discipline) would also dilute any leftward shift in the Senate median.

The bottom panel of Figure 2 depicts a situation where most meritorious individuals are to the left-of-centre. This is effected by shifting the ideological distribution of such people to the left by 1/2 standard deviations. As a consequence, the Conservatives could expect at most one of the 22 appointees to fall to their right, and only 5 such appointees would hold positions between 0 and 1. Thus at most 51 Senators (including the independent Conservative) would hold positions to the right of 0; the Senate median would thus fall just to the left of centre.

We are now in a position to answer the question set out above, that is, how will the Government’s proposed appointment process alter the parliamentary situation. The general answer is that it will shift the Senate median to the left – but by how much depends on the ideological distribution of meritorious individuals (and, to a lesser extent, on the cohesion of the Senate Liberals). If potential appointees are as likely to be right-wing as left-wing, the impact on the Senate median will be minimal; if most such individuals are left-wing, the Liberals’ appointment process may move the Senate median much closer to the Liberals’ position. However, the small number of Liberal Senators does put a limit on how much change the Liberals can effect in this way. Even if the ideological distribution of meritorious individuals were heavily right-skewed such that all 22 appointees were to the left of the Liberals, there would still only be 50 Senators at or to the left of the Liberal position, not enough to push the Senate median to the Liberals’ position. But the Liberals do not require that; to effect their agenda they simply require that the distance between the Senate median and their own position be less than c.

3. Are the Liberals likely to follow through on their merit-based appointment process?

The model establishes conditions under which one can expect the Liberals to break their promise to effect a truly non-partisan, merit-based appointment process.

• c ≥ |LIB-CON|: it is costless for the Liberals to keep their promise because they can effect their legislative agenda regardless of the Conservatives’ Senate majority. Under these conditions, the Liberal proposal for Senate appointments is mere window-dressing.
• c < |LIB-CON| and the ideological distribution of meritorious individuals is symmetric: The Liberals are likely to break their promise under these conditions. This is is because a non-partisan, merit-based appointment process will leave the Senate median close to the Conservatives’ position, allowing the Conservatives to block much of the Liberal agenda. The smaller c is relative to the ideological distance between the two parties, the stronger the incentive for the Liberals to stack the Senate, either overtly or covertly by politicizing the “non-partisan” appointment process.
• c < |LIB-CON| and the ideological distribution of meritorious individuals is right-skewed: The situation is unpredictable. On one hand, by simply keeping their promise, the Liberals would be able to effect a significant leftward shift in the Senate median. If the resulting distance between the Senate median and the Liberals’ position was then less than c, one could expect the Liberals to keep their promise because even a non-partisan appointment process would enable them to effect their legislative agenda. However, were the resulting distance between the Senate median and the Liberals’ position to still be greater than c, the Liberals would likely break their their promise and stack the Senate provided they felt that they could count on the unwavering support of both sitting Liberal Senators and their “non-partisan” appointees.

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In this post, I consider the proportionality of the Alternative Vote (AV), that is, the degree to which AV produces a 1:1 ratio between parties’ vote shares and their seat shares. (AV is the electoral system that is purportedly the Liberal’s favoured alternative to replace Canada’s first-past-the-post electoral system (FPTP).)

By using data from Australian federal elections as well as state elections in Australia’s five mainland states, we can see how AV tends to perform in six different polities.* Moreover, because these jurisdictions all employed FPTP at some point in time, we can also consider whether the shift to AV altered the votes-seats proportionality of Australian elections. This should give us some idea of what to expect should Canada adopt AV.

A priori, we should not expect AV to be any more or less proportional than FPTP. The reason is that both system tend to employ single-member districts. The number of seats per district—what political scientists call the district magnitude—constrains the proportionality of an electoral system quite independently of the formula that is used to translate votes into seats. The higher the district magnitude, the more closely the division of seats among parties can approximate the distribution of vote shares among parties. This improves the votes-seats proportionality of the electoral system. Conversely, votes-seats proportionality that is achievable declines as the district magnitude moves to 1.

Understand that the impact of district magnitude on votes-seats proportionality operates at the district-level. It’s quite possible for an electoral system based on single-member districts to be proportional in aggregate even as it is highly disproportional in every district. Imagine a polity with three parties (A, B, C) competing in FPTP elections in three single-member districts (1,2 3). Assume that party A wins 34% of the vote in district 1 versus 33% for parties B and C, respectively. Similarly, B wins district 2, and C wins district 3, on identical divisions of the vote, that is, 34% – 33% – 33%. The result is a high degree of disproportionality within each district (the party winning 34% of the vote obtaining 100% of the district’s seats) but perfect proportionality in the aggregate, each party winning 1/3 of the seats on 1/3 of the vote.

Of course, district-level disproportionality need not (and often does not) cancel out across districts; it may well be compounded. Indeed, in the past governing parties would intentionally gerrymander and malapportion districts to ensure that disproportionality compounded across districts: district boundaries were drawn to ensure that the government won the vast majority of seats by razor-thin margins whilst the opposition’s votes were concentrated in a few districts which it would win by massive margins. But disproportionality can also be compounded across districts because of how voters cast their votes. In closely contested multi-party elections supporters of 3^rd place parties tend to defect to one of the two leading parties in their district. In the aggregate this results in the top-two vote-winning parties obtaining seat shares in excess of their votes and 3^rd+ place parties obtaining seat shares below their vote shares.

Votes & Seats in Canada under FPTP

Figure 1. (right-click to enlarge)

This pattern is visible in Figure 1, which shows the relationship between vote- and seat-shares at Canadian general elections since 1949. A perfectly proportional electoral system would allocate seat shares to parties such that all outcomes fell on the dashed 45° line, indicating a 1:1 ratio between parties’ vote-shares and seat-shares. Instead, what we see is that the red and blue dots (representing the Liberals and Conservatives, respectively) are consistently above the 45° line whenever their vote-shares exceed 35 percent. Correspondingly (because elections are zero-sum), parties with vote-shares below 35% consistently fall below the 45° line. The few exceptions to this rule are regional parties (notably the Bloc Quebecois and Reform).

We can describe the Canadian data more precisely by regressing parties’ seat-shares (S%_it) on their vote-shares (V%_it) and a set of election-year fixed effects (Y_t):

S%_it = a + bV%_it + dY_t + u_it [1]

Disproportionality is signalled by b ≠ 1. Estimating Eq. 1 via OLS yields

b = 1.28 (.03)

Adj. R² = .88  RMSE = 7.20

N Obs = 119  N Clusters = 22

Huber-White SE clustered by election in parentheses

No surprise here: Canada’s FPTP electoral system is quite disproportional.

It is interesting and informative to modify Eq. 1 to include the square of parties’ vote shares.

S%_it = a + b₁V%_it + b₂V²%_it + dY_t + u_it [1b]

This specification allows for nonlinear and increasing returns to votes. Estimating Eq. 1b via OLS yields:

b₁ = .06 (.11)  b₂ = .028 (.002)

Adj. R² = .95  RMSE = 4.74

N Obs = 119  N Clusters = 22

Huber-White SE clustered by election in parentheses

These results tell us that the marginal effect of votes on seats in Canada increases as the party’s vote-share increases. To be precise, a party’s seat-share increases by .06 + .028V%_it for every 1% of the vote the party wins. So the larger a party’s vote-share, the greater the rate at which it translates votes into seats. In fact, one can deduce that the Canadian system’s “break-even” point is 33.6% of the vote; every 1 percent of the vote won after this point returns greater than 1 percent of seats.

Votes & Seats in Australia

The Canadian data provide a context within which to consider the proportionality of Australia’s AV electoral system. Figure 2 below shows vote shares and seat shares at Australian federal and state elections since 1890. The colour coding in Figure 2 varies by electoral system. So one sees the relationship between votes and seats under not just FPTP and AV but also the Contingent Vote (CV) in Queensland, and STV and 2-round plurality in NSW.

Figure 2. (right-click to enlarge)

I find three things noteworthy about Figure 2.

1. Australian elections are characterized by disproportionality. Observe that parties that obtain 35-40+% of the vote tend to have seat-shares that fall above the 45° line that marks perfect proportionality.
2. Disproportionality at Australian elections does not appear as severe as it is at Canadian elections. It’s really only in Queensland that the return to votes is visibly non-linear and increasing.
3. It’s not obvious on these data that elections under FPTP were significantly more disproportional than those held under AV.

Of course, these are just my impressions of the visual data; it’s worth exploring the data more systematically. Now, in assessing the votes-seats proportionality of Australian elections we want to:

• account for the fact that some of these elections employed multi-member districts;
• allow the relationship between votes and seats to vary by state; and
• identify the impact on proportionality of shifting from FPTP to AV.

I do all this by: i) controlling for the average district magnitude at election t in state j (M_tj); ii) adding state fixed-effects (STATE_j) to the model and interacting these state fixed-effects with parties’ vote-shares (V%_ijt); and iii) including a dummy variable, AV_jt , that equals 1 when AV is used and 0 when FPTP is used. (Elections that employed other electoral systems are dropped.) The model is

S%_iit = a + d₁M_tj + d₂Y_t + d₃STATE_j + b₁V%_ijt + b₂(V%_ijt * STATE_j) [2]

+ b₃(V%_ijt * AV_jt) + b₄(V%_ijt * STATE_j * AV_jt) + e_ijt.

The quantity of interest here remains the marginal effect of votes on seats, that is, the rate at which vote-shares are translated into seat-shares. The interactions between V%_ijt and STATE_j and AV_jt in Eq 2 allow this rate to vary by state and by electoral system.

Figure 3. (right-click to enlarge)

Figure 3 shows the marginal effect of votes on seats for each state under FPTP and AV. The circles represent the point estimates, and the bars show the 90% confidence intervals surrounding these estimates. So what Figure 3 tells us, for example, is that for every 1% of the vote a party won at elections to the Commonwealth’s House of Representatives (COM-HR) it obtained about 1.08% of the assembly’s seats on average. In other words, Australian federal elections are mildly disproportional. Furthermore, the proximity of the blue and gray dots tells us that the relationship between votes and seats at Commonwealth elections was unaffected by the shift from FPTP to AV.

In the main, the same remarks can be extended to all five mainland states. Only Victorian elections – held under FPTP no less – might, maybe have been proportional. In no state did AV make elections reliably more proportional – though it came close to doing so in Western Australia. Of course, Australian elections were never as disproportional as Canadian federal elections; only elections in Queensland come close – and that probably has a lot more to do with how the Nicklin and Bjelke-Petersen governments malapportioned and gerrymandered electoral districts than the electoral system itself.

To better isolate any causal effect of the electoral system on votes-seats disproportionality, I estimated Eq. 2 again, but with the data limited to just the very last elections held under FPTP and the elections held immediately thereafter on the adoption of AV. This eliminated NSW from the analysis (because NSW experimented with several electoral systems between abandoning FPTP and adopting AV). District magnitudes did not vary within states at these transitional elections, so there was also no need to control for the average district magnitude. The model was then:

S%_iit = a + d₁STATE_j + b₁V%_ijt + b₂(V%_ijt * AV_jt) + e_ijt [2b]

Under this model, the marginal effect of vote-shares on seat-shares under FPTP is given by b₁, whilst under AV it’s given by b₁ + b₂. Estimating Eq. 2 via OLS returned 

b₁ = 1.10 (.04)  b₂ = -.04 (.08)

Adj. R² = .88  RMSE = 8.51

N Obs = 47  N Clusters = 10

Huber-White SE clustered by election in parentheses

Thus the ratio of vote- to seat-shares was 1:1.10 under FPTP and declined to 1:1.06 under AV – BUT this decline is not statistically significant (not by a long-shot). In other words, we can’t rule out that the shift to AV made no difference whatsoever.

Finally, I estimated an Australian analogue to Eq 1b. containing parties’ vote shares and their squared vote shares – but only using data from AV elections:

S%_iit = a + d₁Y_t + d₂STATE_j + b₁V%_ijt + b₂V²%_ijt + e_ijt [3]

Estimating Eq. 3 via OLS yields:

b₁ = .89 (.06)  b₂ = .004 (.0016)

Adj. R² = .88  RMSE = 6.56

N Obs = 1209  N Clusters = 180

Huber-White SE clustered by election in parentheses

These results indicate that AV also generates nonlinear and increasing returns to votes, although not nearly so sharply as in Canada.  The “break-even” point under AV is also lower at 27.5%

Discussion

There’s no reason to expect AV to be any more proportional an electoral system than FPTP. This is because the proportionality of the electoral system is tightly constrained by the number of seats per district, and both AV and FPTP are typically used with single-member districts.

The data from Australian state and federal elections are consistent with this theoretical expectation. Australian elections do not produce the level of disproportionality that is observed in Canadian elections – but this probably has little to do with Australia’s AV electoral system because the adoption of AV in favour of FPTP in Australia had no discernible impact on electoral disproportionality.

What does this mean for electoral reform in Canada? These data suggest that we should not expect the disproportionality of the Canadian electoral system to change appreciably were the Government to choose AV to replace FPTP. Disproportionality systematically favours larger parties over smaller parties, and to that extent the Conservatives should not be particularly apprehensive of a transition to AV. As I observed previously, a shift to AV could position the Conservatives as a right-wing version of the ALP – not often in government, but dominant on their part of the political spectrum. Correspondingly, the NDP and the Greens should not expect an AV electoral system on its own to improve the efficiency with which these two parties translate votes into seats.

In my next post I’ll explore another aspect of AV – it’s volatility.

* A big thanks to my colleague, Campbell Sharman for furnishing me with these data.

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