Although it’s difficult to predict many aspects of Egypt’s upcoming election, most observers assume that the Muslim Brotherhood’s Freedom and Justice Party will win a plurality of seats, while the smaller, divided liberal parties will perform poorly.  This is most likely true.  What is not true, however, is the often-stated proposition that this is partially because the country’s electoral system works to the Brotherhood’s advantage.   There are some good reasons people have said this.  Under previous versions of the electoral law, I’ve made the same argument.   As the rules stand now, however, this is not completely true.   The details of the new electoral system, specifically the seat allocation method in the proportional tier, will give actually give a boost to the fractured liberal parties, while depriving the Brotherhood of a majority they would obtain in more commonly used electoral systems.  The reason for this is due to the formula used to calculate who wins the two-thirds of seats in the proportional representation tier.

No proportional representation system can perfectly award seats in one-to-one relation to vote shares. There are various systems for allocating seats proportionally but broadly speaking, they all fall into two categories: the largest remainder method (which Egypt uses), and the highest average method.  For the largest remainder method, each seat in a legislature corresponds to a raw number of votes, equal to a quota, and a party’s seat share depends on the number of quotas it wins in an election.  How that quota is calculated varies based on the system, but under the simplest method, the Hare quota,  total votes are divided by N (total) seats to create a quota used for allocation.  After this number is calculated, parties are awarded seats for every time they reach that quota.  However, after the quota is reached a certain number of times, there are bound to be some seats left over, as well as remainder votes that didn’t contribute to a full quota. Parties’ remainder votes are then tallied and used to determine who will get the remaining seats.

For the upcoming elections, it appears Egypt will use a Hare quota.  Despite its recent use in Tunisia, the Hare quota is a somewhat unpopular method. Figure one shows that the largest remainder method, and the Hare quota specifically, isn’t nearly as common as the highest average method of seat allocation.  I bring this up because it’s notable the government chose a less common system.

Figure one

Hare quotas may be less popular because, while being easier to understand, they are slightly less proportional than other systems. In general, Hare quota’s favor smaller parties, and produce more fractured parliaments.  In the case of Egypt, it will benefit smaller parties.  To illustrate this, let’s look at how the Hare quota will play out.  In Figure two, I made a very crude estimate of a hypothetical vote distribution in one of Cairo’s four districts (with a district magnitude of ten). For vote totals, I divided how well each party was doing in the most recent public opinion survey by the total voters.  My total voters was calculated by taking how many Cairo voters participated in the March referendum and dividing by four (the number of districts in Cairo).  The problem with this, of course, is that I’m using a national poll and placing it at a district level. Unless somebody is willing to provide me with crosstabs, however, this is the best I can do.  First the Hare quota is calculated (576,640/N (10)), which equals 57,664.  This is the number of votes a party needs to get one seat in the first distribution. After this, however, we still have five more seats to allocate.  So the remainders are then ordered from highest to lowest, and the five parties with the highest remainders are given one extra seat.

Figure two (Click to enlarge)

Freedom and Justice gets four seats, Al-Wafd gets two, and the remaining four seats go to the next four parties. Note that in this scenario, Freedom and Justice isn’t being specifically disadvantaged; they are actually receiving the number of seats they deserve. It’s just that smaller parties, are getting more seats than we would expect if the system was perfectly proportional.

Now let’s look at how the exact same scenario would turn out if we used the much more common, highest average method.  Specifically, the D’Hondt system, which is the most common method used across the world.  Figure three below shows how this works.  Party votes are first divided by 1, then 2, then 3, and so on until they reach N number of seats in the district.  So in our Cairo district, they would keep dividing untill they reached ten.  This produces the chart we see below. After this, the N (in this case, ten) highest distributions are found, and each one awards that party a seat.   As we can see below, this method give Freedom and Justice six seats in total, Al-Wafd three, and Al-Nour one.  In this case, Freedom and Justice overperforms, while the other parties generally get what should be expected.

Figure three (Click to enlarge)

It should also be noted that this method would favor Freedom and Justice even more in smaller Egyptian districts.  Under the D’Hondt method, a decrease in districts magnitude can decrease the number of parties who win a seat.  If, for example, this was a rural district in Masa Matruh Governorate, with four seats, then Freedom and Justice would get three seats and Wafd one.

There are several interpretations of why the SCAF would choose the largest remainder method.  The first is that they were simply using the system closest to what was used the last time Egypt had PR elections, in the 1980s. (1) This would seem plausible.  A second interpretation is that this is an attempt to weaken the Muslim Brotherhood, whom they knew would be the largest party.  (Perhaps the Tunisian transitional authority made the same calculation with regards to weakening Enahda’s seat total).  A third interpretation is that the SCAF wants to reduce the number of wasted votes (votes cast for a party that doesn’t enter parliament).  A high number of wasted votes could jeopardize the legitimacy of the election in the eyes of many Egyptians.  A fourth, very cynically theory that I don’t actually believe, is that the SCAF is intentionally trying to create a parliament that is as fractured and weak as possible.  The SCAF’s reluctance to abolish the nominal tier of seats, which most people predict will be won predominately by independents; the low .5% threshold for entering parliament; and the Hare quota, are all rules that will favor a greater quantity of small parties, and MPs with no party affiliation.   This could create a parliament that is weak and ineffective, either creating a strong president, or  weakening the public’s trust in democratic institutions.  An extreme cynic could argue that both of these would benefit the SCAF.

I’m more inclined to believe in the first explanation, and think that a large number of wasted votes is greater threat to the legitimacy of the election than a fractured parliament. Regardless of why these rules were chosen, however, it’s important to realize the implications they will have.

(1) In 1984 and 1987, Egypt used a modified Hare Quota, where seats that could not be awarded on the basis of full quotas were awarded to whichever party had at least half a quota. When no party achieved this cutoff, such seats were awarded to the nationally most popular party. This was a very unproportional way to allocate remainders, and served to boost the seat total of Mubarak’s National Democratic Party.