The following is a guest post from Dartmouth College political scientist John Carey. John notes that “This TMC contribution is based on a paper that presents the full, simulated results of Tunisia’s 2011 election under various PR formulas, plus more analysis. I will post the paper to my website soon, but I am traveling and temporarily unable to update the site. If you want to look at the paper, email me at firstname.lastname@example.org — I’m happy to send a copy.”
In 2011, Tunisia held the first post-Arab Spring election, for 217 members of its Constituent Assembly, in 33 electoral districts, by closed-list proportional representation. The Assembly is slated to produce a constitution and put it before voters for ratification this year, followed by elections for a new parliament (and possibly also for a president, depending on the structure of the constitution). The 2011 results show that what PR formula is used in the next election could be critical, but also that what was best in 2011 might well be the wrong recipe for subsequent parliaments.
The formula used in 2011, Hare Quota with Largest Remainders (HQ-LR), was pivotal to the outcome of that election, in which the largest party, the Islamist Ennahda, was awarded less than a majority of seats and therefore has had to negotiate with other groups in drafting a constitution. Simulations of electoral outcomes using district-level data show that, had the other most commonly used PR electoral formula been employed, Ennahda would have been awarded a super-majority in the Assembly and been in a position to impose a constitution. Whether by design or not, the dispersal of power among alliances in the Assembly was fortuitous at Tunisia’s “constitutional moment.” Going forward, however, the incentives for party system fragmentation generated by HQ-LR could impede the development of a workable party system, and Tunisian reformers should consider replacing HQ-LR with a divisor-based formula.
In the world of PR, there are two main families of formulas for converting votes to seats: quota and remainders (Q&R) methods, and divisor methods. The basic principle of Q&R is to set a “retail price,” in votes, at which seats in each electoral district may be purchased by party lists, with that price then subtracted from a list’s account for each seat. As soon as no list’s account exceeds the retail price, any remaining seats are allocated, one per list, in order of the lists’ remaining votes. Lists that win seats on the basis of their remainders are, effectively, buying seats wholesale, for fewer votes than those purchased by full quota. Divisors methods operate according to a different principle, dividing lists’ vote tallies by a sequence of numbers to establish a matrix of quotients, then allocating seats in descending order of quotients until all the seats in a given district are awarded.
The key point is that Q&R approaches create two separate pricing schemes for winning seats, whereas divisor systems do not. Under divisors systems, the best way for lists to win seats is to be bigger, period. Small lists stand to gain by coalescing into bigger alliances. Under Q&R, this is not necessarily so. Under some conditions, the separate pricing schemes can generate incentives for lists to “hunt remainders” – that is to forego coalitions that would put them into the retail market for seats and instead to remain apart, pursuing seats only on the remainders market. The structure of competition in Tunisia so far suggests that these pro-fragmentation conditions apply.
The irony in suggesting that HQ-LR may be a problem for the development of Tunisian democracy going forward is that it was almost certainly a blessing in 2011. The figure below shows vote shares (blue bars), seat shares under HQ-LR (red bars), and simulated seat shares under DHD (green bars), among alliances that won representation in the Constituent Assembly. There are a few key things to note. First, Ennahda was the dominant party, an electoral Goliath with almost 40% of the vote beset by a field of Davids, none of which won even 10%. Second, almost every party that won any seats got a ‘bonus’ – a seat share greater than its vote share – mainly because more than 20% of the votes were split among the more that 500 lists that won no representation. Third, among top handful of lists, the bonuses were relatively equally distributed (4-6%) despite the fact that Ennahda’s vote share dwarfed those of the others. Finally, had Tunisia used DHD, the most common divisor formula, Ennahda would have captured nearly all the seat bonus itself, winning 69% of the seats.
The next figure provides another way to visualize the difference between HQ-LR and DHD for the 2011 election, plotting the difference between the seat bonuses for each list under the two systems against the list’s national vote share. Points above zero (colored green) represent alliances that did better under HQ-LR than they would have under DHD; those below zero (colored red), by contrast, would have fared better under DHD; whereas the blue points represent alliances whose bonus (or penalty) was equivalent under both rules. The X-axis in Figure 5 is reversed, such that reading from left to right moves from larger alliances to smaller, and is shown on a log scale to avoid clustering the abundant observations with small vote totals all on top of each other.
The most remarkable characteristic of the seat bonuses generated by HQ-LR is the extent to which they accrued to small rather than large alliances. This distributive effect resulted from the Goliath-versus-multiple-Davids structure of competition in the 2011 election. Paying retail for most of its seats drained Ennahda’s coffers of votes, opening the way for the smaller contenders to buy seats at prices far below what Ennahda was paying, and capture the vast bulk of the available seat bonuses.
This result was fortunate in 2011, unusual by comparative standards, and potentially problematic for the future. It was fortunate because, by leaving Ennahda short of a majority, the result forced Tunisia’s Goliath to negotiate with other alliances in the Constituent Assembly. At constitutional moments, systems of representation that disperse power and foster inclusiveness tend to yield more stable charters of government. It was unusual insofar as seat bonuses generally rise with vote shares under all electoral formulas – even HQ-LR in most environments. But it was troubling in that, if Tunisia maintains HQ-LR, its competitive structure could perpetuate incentives for Ennahda’s small competitors not to coalesce, thus locking in a high level of party fragmentation and inhibiting the formation of a viable competitor to Ennahda.
Vote fragmentation will likely diminish somewhat in future elections, whatever formula is used, because many of the hundreds of lists that gained no traction among voters in 2011 will not persist. HQ-LR’s incentives against coalescing, however, are strongest not for the absolutely hopeless lists, but for those that can capture vote shares large enough to contend for remainders seats but not large enough to contend to govern. In this light, consider that in the 2011 election, Ennahda bought 69% of its seats at retail, but its opponents, as a group, bought just 11% of their seats at retail and picked up the other 89% on remainders. Most of those parties are more secular and liberal than Ennahda so one might expect them naturally to gravitate toward alliance to present an alternative government. But under HQ-LR, coalescing would undermine the efficiency with which the non-Ennahda lists convert votes into seats.
The simulated results demonstrate that DHD, the most widely used divisors-based formula, would have produced a distorted result if applied in 2011, massively over-representing Ennahda. That’s because DHD, among the various divisors formulas, most heavily favors the largest competitor, and does so particularly when the gap between the largest and the next is wide. In that sense, Tunisia in 2011 represented a perfect storm scenario for a winner’s bonus under DHD. But DHD is not the only option for a divisors-based formula. The St. Lague divisor would have delivered a much smaller bonus to Ennahda. Just as importantly, divisors formulas would not generate incentives for remainders hunting because they do not set up two separate markets for seats – retail and wholesale – with large lists frequenting one market and small lists the other. As a result, a divisors-based formula would encourage Tunisia’s fragmented opposition to coalesce, rewarding groups that did, which would further limit the size of the winner’s bonus.
Tunisia’s 2011 was by far the most successful of the Arab Spring so far, in part because the leaders who chose HQ-LR for that founding election chose well. Furthermore, there are signs that the Constituent Assembly selected in that election, and working in the context of negotiation and compromise it produced, has made some good initial decisions on many important counts (see Fish and Michel 2012). What is best for founding elections, however, is not necessarily ideal for subsequent rounds. As Tunisia moves from its constitutional moment to the long series of governing moments that should follow, it should consider replacing HQ-LR with a divisors-based formula that encourages the formation of broad electoral alliances, not remainders hunting.