The Moorish Wanderer

Across Partisan Lines: Redistricting in Morocco

I apologise in advance to the excessive level of abstract models used in this post, but there is only so much I can take in the current, mainstream political science discourse in Morocco. I mean, I am a great fan of Wijhat Nadar (the review) and writings of heavyweights like Abdellah Laroui, but it would be fun to explore other alternatives, possibly using teachings from game theory. Plus this is High School-level math, so no harm done.

A quick look at a relatively unearthed matter in Moroccan politics can always tell when a consensus crosses party lines, and in this case, it is about the number of seats allocated to each district. Traditionally each and every party vent their respective grievances as to the incumbent districting: smaller parties vehemently oppose high thresholds (PSU found an eloquent advocate against it back in 2007 in one of its prominent leaders, Mohamed Sassi) and larger parties tend to believe their strongholds are undervalued: back then it was USFP in Rabat or Casablanca, nowadays it is PJD in Tangier, Casablanca or Salé. Every election is the same, parties complain to the media, but cannot agree on anything.

In fairness, districting is always a zero-sum game, even if the number of seats in parliament is expanded: a large district benefits some type of parties, and harms others. Better still, some parties have contradicting interests on similar constituencies; for instance, the 2011 general elections pitted Istiqlal and USFP (in Fez), PJD and UC (Marrakesh) RNI and Istiqlal (Southern seats) among others. A slight change in the number of seats, or inter-province districting can tip the balance one way or the other. Political parties in Morocco do look (and act) disorganised and utterly incompetent, but this belies their inner rationality as to their political survival.

Consider a simple model to capture the perverse effect that compels political parties to defer to a benevolent actor e.g. the Interior Ministry. It is the rational course of action for every political party in Morocco: abdicate the possibility of a contentious (but ultimately more democratic) battle over the optimal number of allocated seats per district, for a more peaceful, consensual redistricting under the auspices of a mechanism-designer with endogenous preferences, ultimately the perpetual weakening of that very same political spectrum.

Consider a number of n political parties competing for a fixed (but undefined) number of seats. Each party i derives some utility from contesting elections and having members of parliament elected; three layers of benefits can be listed: first, merely electing a member of parliament, second, electing a caucus with at least 6% of nationwide popular votes, and finally, a benefit from coming on top, or very close. The utility function is thus:

U(h_i) = \mathbf{1}_{v(h_{i,6})}\{\pi(h_i)+\phi h_i - \max\{h_{-i}\}\}+\frac{v(h_i)}{v(n)} -c_0

As each party prepares to contest elections, they face a certain fixed cost (typically the deposit required from each and every party candidate/list) but on the other hand, there are benefits attached to large caucuses, either in form of increased monetary compensation, or some utility derived from participating in a government. A simple differentiation pinpoints exactly the conflict of interest:

\dfrac{\partial U(h_i)}{\partial h_i}=\pi'(h_i)+\phi-\max{h_i}=0

that is:


As one can see, the benefit from one additional seat for a particular party stems from the performance of other parties (a primary evidence of the zero-sum aspect of game elections) and most importantly, is negatively linked to this term \phi. In this particular setting, it refers to a ‘premium’ put on the seat(s) won by that particular party. As it shall be proven later, each and every party has a particular incentive at keeping that parameter exogenous – in this case, defer to a higher authority.

Suppose the premium is set by the final outcome, i.e. suppose the present electoral result decides the next performance and the size of the district. This means:



\pi'(h_i)=\max{h_i}-[\phi'(h_i) + \phi(i)]

Now, there are a couple of cases where the last term might differ from the first case to the second. And there comes the Interior Ministry (the shiny knight cloaked in white, one might say) in providing an arbitrage that benefits individual parties, but ultimately harm their collective chances in getting large, stable government coalitions. In this setting, individual parties are better off when the premium is low, in fact when it is lower than the fixed, exogenous term \phi, that is:


Because of the higher competition (captured by a competitive districting) between parties mean the overall benefit from seats won by a particular party is diminished, and coming on top is not worth much.

As the same reasoning is applied to the entire caucus carried by party i, we get:

\int \phi'(h_i)+\phi(h_i)d h_i \geq \phi \int h_i d h_i

and there is your proof: on average, a caucus is better off when the districting is exogenous: \mathbb{E}(\phi(h_i))\geq\phi\mathbb{E}(h_i) this is possible because each district is treated the same; the intuition behind it is, preferential treatment for one district cannot be achieved because every other district will have to be treated similarly, and that takes us back to square one. The best response for each political party is thus to support uniform treatment, and as a result their respective caucuses are weakly better of with an exogenous districting.

Suppose we also look at the dispersion of caucuses as well: a larger expectation in caucus size does not mean both cases exhibit equal dispersion around it; in fact, since h_i denotes dispersion around the mean, and since: 2 h_i \phi'(h_i)+ h_i^2\phi(h_i)\geq \phi'(h_i)+\phi(h_i) then \mathbb{V}[\phi(h_i)]\geq\phi^2 \mathbb{V}(h_i)

This is an important result, because individual party interest trumps the collective likelihood of having a strong parliamentary majority (due to competitive districting) and the benevolent designer can only minimise the volatility – if it is indeed in their interest.

A candid observer cannot but wonder how Makhzen and Nihilist parties seem to agree on  a status-quo that harms representative democracy: true, smaller parties (including PSU) are most likely to be wiped out of the political map if they do not merge or join larger parties, but on the other hand, larger parties also seem to know they are next in line, because the bulk of their seats can be lost if a competitive system were to be introduced, be it an alternative ballot system, or an unfavourable (but impartial) districting.

Authorities on the other hand seem to have some incentive in keeping volatility high enough, so as to deny any potentially rebellious party the possibility of commanding an absolute majority, and hence forming an independent-minded government. It seems political rationality in this setting trumps every possible narrative about ideology, or political history.