# The Moorish Wanderer

## The Next USFP Premier

It lives! Driss Lachgar has been elected as USFP next boss. A great victory for Game Theory applied to Moroccan politics, and a great victory for the new political order in Morocco.

His moustache is not a new fashion, mind you.

I should perhaps begin by addressing some issues about the numbers: I am still not sure about the total number of party delegates (1,200? 2,000?) though I am enclined to think the total number of votes was close to 1,600 for both ballots. Other than that, my predictions were broadly vindicated: party delegates chose overwhelmingly parliamentary candidates, and the fact that Mr Oualalou failed to muster enough support to carry him through the second ballot translated automatically into a Lachgar coronation.

Furthermore, I suppose Mr Zaidi was hurt by Mr Malki’s candidacy: indeed, I have assumed delegates had some ranking of their choices, and they move to their second choice when their first did not make it through the first ballot. I have further assumed delegates supporting parliamentary candidates prefer would automatically prefer to vote for Mr Oualalou as a second choice, should he make it to the second ballot. It also appears Mr Lachgar was the main beneficiary of these second or third choices, respectively for Mr Oualalou and Mr Malki supporters.

And now to the political conclusions of tonight: This election, I would argue, signifies the end of intellectual politics in the Moroccan political discourse, and especially in a party that prides itself as a cornucopia of intellectuals and thinkers. And though Mr Lachgar is perhaps has a great deal of education (he is a Lawyer after all) he represents, with Messrs Chabat (PI) and Benkirane (PJD) the very idea of anti-intellectualism, and fully embodies populism as an efficient political strategy.

I also argue this is not as bad as it looks for Moroccan representative democracy: It would be foolish to expect our present political system to produce beacons of integrity, thoughtfulness, honesty and competence. On the other hand, the system rewards those with acute instincts for political survivals, and a large subset of the electoral has confirmed the trend. Now, three populist party bosses means Moroccan politics will be a lot livelier than the past decade, which is always good, and it also creates among the electorate, not a new hope, but some level of expectation. And this is the party where democracy, and ultimately citizens, get their rewards.

As I have mentioned before, these populist exhibit remarkable instincts for political survivals, and their rationality is not to be underestimated (whatever numerology mumbo-jumbo Mr Chabat fancies) they do know they cannot promise what they cannot deliver. They also know the limitations of their own political power; the rational course of action would be to look for professional advice, operatives and specialists to support them in their venture to revolutionise Moroccan politics. Indeed, let us not forget they are all in a quest against some corrupt establishment (though they deny charges of disestablishmentarianism)

## Who Will Get The Big Job?

Posted in Flash News, Morocco, Read & Heard by Zouhair Baghough on December 10, 2012

5 candidates are competing to replace the dean of representatives and incumbent USFP premier, Abdelouahed Radi. 5 candidates with similar and different views, no doubt. And I thought this is the chance to assume, then prove political agents in Morocco are capable of rational strategies and decisions – and that will be put to the test, on the weekend 14-16th of december.

This is textbook game theory, where the game is as simple as it gets: during USFP’s convention, the delegates from all over Morocco need to vote for the candidate they believe can lead them to victory in 2016, or at least be in position to share some of the spoils a strong contender generates. I would like to think the centre-left party would do some introspective thinking about its political philosophy, its alliance strategy, but the would-be leaders would be hard-pressed to deliver results. So, setting aside the assumption of a selfless leader eady to sacrifice their (his) political future for the sake of the party, I would posit all 5 candidates have every incentive to go for -at least implicitely- an immediate positive return.

As mentioned before, the voting game is about declaring preferences. So it is quite possible the next USFP convention would end up in a deadlock – although it has a very low probability of happening:

$\mathbb{P}(deadlock)=1-\frac{\max {V}_{i=1}^5}{5!}$

(5! is the factorial, with a value 120, as there are 120 different combinations of listing preferences)

and even lower probability if USFP delegates are very adverse to rowdy convention outcomes (and recent history shows), ie. $u\left[\mathbb{P}(deadlock)\right]$ where u(.) is strictly concave to denote this risk aversion.

For each delegate thus, there is a ranking, I would like to add to a small constraint: the delegate has a strong preference for the first choice, their candidate, and then enunciate weak preferences for the remaining four:

$V_1 \succ V_2 \succeq V_3 \succeq V_4 \succeq V_5$

An equilibrium (the election outcome) does not necessarily mean a majority of delegates select the same first choice. To illustrate this, assume the rules of elections have been altered. Instead, the party convention will go through 5 ballots, each candidate is submitted to approval or rejection. The equilibrium here depends on the candidate order. This step is simply internalised by each and every delegate: they weigh in different outcomes, and eventually come up with a choice that maximizes a series of objectives (party victory, personal gain, idealistic aims, etc.) their respective preferences are solved using backward induction.

Since party convention rules for two ballots, preferences will be broken down in first-hand choices, and second-hand choices if the former fails.

Let us now consider more down-to-earth elements of this election: presumably, USFP needs a strong leader to measure up to Hamid Chabat, or Hakim Benchemas, or indeed the Head of Government, Abdelilah Benkirane. Meaning their next Secretary General has to adopt opposition-like strategies, including:

1/ Very active and visible on the media

3/ A member of parliament (MP)

Point 2 and 3 are correlated – a member of parliament has a privileged access to mainstream media an outsider lacks. As it turns out, this rules out two candidates, Fathallah Oualalou and Mohamed Talbi (Zaidi, Lachguar and Malki being all three representatives) to be first choice for a whole lot of delegates. In fact, the weight party delegate allocate to this quality (being an MP) is roughly equal to the percentage of those delegates whose preferences are based upon that criterion: what is the probability of choosing a member of parliament as a first choice. answer: 60%. That is not to say 60% of the delegates will chose between Zaidi, Lachguar or Malki, but each delegate has a 60% chance of of choosing one of these candidates. But since it is expected some 1200 delegates will attend the convention, my assumption would be that 720 delegates will vote for one of the three ‘premium candidates’, and then scramble for the remaining 480 that votes primarily for the two other candidates, on the second ballot.

Let me make an assumption about the 480 ‘idealists’: presumably, a large percentage of those will vote for Fathallah Oualalou, and his votes will be crucial for the two parliamentary contenders. Notice I mention two, and not three. The proof is in three steps: first, assume all three candidates have equiprobability of getting the 720 votes – this means on average each one gets 240. A winner needs to get at least 361 additional votes, so the other 480 votes are not going to be split evenly across the first three contenders, which means only the first two of the parliamentary contenders really matter.

The crucial player in the two-ballots game is thus M. Oualalou: if he comes in second or first in the first ballot, he will be elected on the second,his support has every incentive to stick by him, in addition, support from his parliamentary competitor’s rivals will consolidate his lead. This is based on the assumption that delegates supporting a parliamentary candidate on the first ballot rank the other two behind M. Oualalou.

On the other hand, if M. Oualalou comes in as a third candidate, his support might make a difference. This is because one of the parliamentary contenders in the run-off could be too polarizing, and even support transferred from M. Oualalou might not be enough. This leads me to lay out some assumption about M. Driss Lachguar, whose own record shows he can be a serious contender, but his polarizing figure could produce a backlash and elevate another, ‘Dark Horse’ candidate to the Premier position.

In many respects, Mr. Lachguar is favoured to be USFP’s next boss: he is a member of parliament, has been involved in the decision to withdraw USFP from coalition talks and join in the Opposition, and rattled sabres over the appointment of M. Karim Guellab as Speaker of Parliament House. Yet many party delegate might not be interested to vote for him on the second ballot (that is, if he makes a first, or close second) and could vote for another, less illustrious candidate in an “Anti-Lachguar” stampede. And yet, there is a chance a Lachguar-Oualalou ticket might get a win, provided the following conditions:

1/ Lachguar supporters stick by him on the second ballot
2/ There is a common pool of Lachguar-Oualalou supporters
3/ Lachguar supporters are expected to cast slightly more votes than Oualalou’s

In fact, the minimum number of Oualalou supporters among the 480 delegates ready to switch on the second ballot, described earlier would be:

$240+480\times\alpha-\alpha^2\times (V_{FO},V_{DL})$

(this is assumed to differentiate between core Oualalou supporters and those likely to switch support to Lachguar

a simple FOC gives: $\max_\alpha V(FO,DL)= \dfrac{\partial V(FO,DL)}{\partial \alpha}=0$ yields $\hat{\alpha}=19.1\%$ so Lachguar only needs 20% of Oualalou’s supporters to throw their support behind him to win the ballot, should Lachguar come a close first or second.

## 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:

$\pi'(h_i)=\max{h_i}-\phi$

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:

$\pi'(h_i)=\max{h_i}-\phi$

becomes

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

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:

$\phi'(h_i)+\phi(h_i)\geq\phi$

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.

## Game Theory & Revolutions

Posted in Flash News, The Wanderer, Tiny bit of Politics by Zouhair Baghough on February 5, 2011

True to my word to Afrinomad, I’ll try and  delineate the game theory applications on revolutions. I’ll go slower, not the least because it’s uncharted territory there to me. I mean, the best I’d ever do with game theory is with economics application -just like the mess I am supposed to sort out by this spring-. This does not mean I don’t understand what I should be posting about. Let’s just say that there are some areas in political sciences I would do well to read about on my spare time (oh? Do I still have one of these?)

Looking back at the undergraduate days, I read an interesting book, which turned out to be a big helper in understanding political sociology: ‘Théorie du Choix Révolutionnaire‘ (T.Tazdaït, R.Nessah La Découverte, 2008). It is handy, in the sense that both authors are at ease with game theory concepts. And one of the many things I noticed -and recorded- was the constant reminder that revolutions, in essence are not really a rational behaviour. Why should it be? The whole idea of mixing revolution theory and rationalism seems ludicrous: not that both concepts are irreconcilable, but because that a pure rationale, from an individual point of view, collective action is deemed to failure. Shaw proposed the following the illustrate the paradox: let the following linear equation be an agent’s utility function R = p.B – C + D

where R is the utility pay-off, p is the probability assigned to the effect the individual can have on a successful outcome for the revolution, C the cost of participation and D the expected pay-off. Before I go any further, this is not a normative model, in the sense that it should not elicit conclusions about what’s a good or a bad revolution. At best, it’s an abstract speculation on rationale behind individual and collective behaviour. Now, if there are masses of people supporting the revolution, an individual contribution to success is next to nothing. Plus if the individual does not participate, they incur no cost and benefit nonetheless from the revolutionary outcome. But if the same result was to be applied to every single member of the community, the revolution is doomed before it even begins. So there is the nodal problem: Revolutions are the deed of the multitude. And yet, when individuals weight in the costs and benefits, they have every incentive to adopt a free-rider behaviour: wait by and look on as he events undo the incumbent regime, then reap the benefits when it succeeds. If not, being obedient brings benefits too.

This ultra-rational behaviour does not explain why revolutions occur. In fact, it just makes people think that revolutions are inherently irrational. But are they? Perhaps this individual methodology is no good to understand collective action: it is logical to assume that the collective effort is not a mere aggregation of individual wills, that, past a certain critical mass effect, it subsumes it and exceeds to a greater strength.

Let’s find us some practical game theory application on Egypt and Tunisia: assume the revolution is a public good – there’s an interesting configuration by Vickery-Clarke-Groves which seems to me suitable for collective actions. In a game theory setting, for a revolution to succeed, it needs to devise some modus operandi following which the result would be strategy-proof, i.e. at some stage, all individuals would contribute to the outcome according to their true needs, and as such their benefits would be larger in contributing to the revolution than just standing out of it, when they would indeed benefit from a change of regime. Let me re-formulate it: there’s a need for a modus operandi such that those really in need for a revolution would in fact contribute rather than just stand by. These very individuals, the least endowed in a given society that is, have every incentive to revolt because the expected loss is considered to be lower than the benefits.

So, a public good, or a revolution, seeks the modified optimization program:

it’s easier to understand than it looks actually – the revolution seeks increasing the well-being of the majority -thus the mode- (first line) but takes ‘taxes’ out of different individuals (second line), and these taxes can be perfectly random, like death, or an injury or just a burned car. k is the last outcome: success (1) or failure (0). Then, at individual level (third line), they have types that are more or less attached to a change in the political regime or indeed achieving any desired outcome the incumbent government does not provide. Insofar the poorest elements have the lowest tolerance for a certain array of imbalanced distribution of wealth, income, power and other social symbolism outlets, they can be expected to react and contribute -issues of coordination are not discussed here- because in Egypt or Tunisia their numbers were important, the contribution of middle classes was perhaps marginal at the second level, but it nonetheless gave a larger boost to the public good. The game has a social choice function f(.) fully strategy-proof as long as it meets the following requirements:

basically, a function that yields a utility such that it is better for an individual to act following their type rather than portray another one (called the incentive compatibility).

When the coordination issue is not discussed, the key for revolutions, from a game theory perspective, is to ask first off, how wide is the gap between expected gains the rioter, soon-to-be revolutionary, is betting on, and their present wealth, and second, how many of them are ready to join in, i.e. how many are in the same position.

When coordination does arise, it can either be the fact of institutional nature -which game theory has little to do with- like pre-existing trade-unions, or the use of social networks (virtual or not), and that is a matter of algorithmic nature, on which I claim no informed knowledge. In any case, coordination in game theory assumes the existence of a benevolent referee which Tunisia and Egypt proved to be non-existent or negligible.

The whole exercise is pointless, save perhaps the idea that revolutions are not inherently dysfunctional occurrences of otherwise rational institutions and behaviour. With a bit of game theory, it can be proven that it is fully rational, and that the only problems in completing the argument are not related to reason, and could nonetheless be expected with the help of otherwise more randomized experiences.

## The Good, The Bad, The Ugly & The Game Theory

Posted in Dismal Economics, Read & Heard, The Wanderer by Zouhair Baghough on February 2, 2011

Though weather is manageable, I caught a cold. Not worrying, but I might be needing a rest, at a moment I need it the least: Game Theory is getting stiff: The conditions for a strategy-proof monetary policy are trickier than assumed, but hey, I shall be posting on that very shortly.

I was just rewatching “The Good The Bad & The Ugly” by Sergio Leone. There are movies that one can never get enough of watching over and over again, and Leone’s tetralogy are no exception. I particularly like the last scene, where Tuco (Ellie Walach), Angel/Sentenza (Lee Van Cliff) and Blondie (Clint Eastwood) compete remorselessly for a treasure left by confederate troops.

The scene I am referring to is the final duel, when the three protagonists face each other, and set on killing for the confederate gold worth $200,000. Actually, I was listening to the movie while working on Osborne’s ‘Game Theory’ (I know, it is not much productive, but there are bad habits one enjoys thoroughly) I could not help myself but to link both things: isn’t the final scene a good illustration for game theory? Since many of my friends advised me to write lighter pieces, I shall use this one as an experiment: how to do some game theory with Sergio Leone (and your humble servant too) There are three duellers: The Good (Blondie), The Bad (Sentenza) and the Ugly (Tuco). They compete for a certain amount of money ($ 200,000), hidden in a certain tomb, whose name’s Blondie (the Good) wrote on a piece of rock. In essence, all players are equal, due to the fact that they have the same amount of ammunition, and when they shoot, they cannot fire quickly enough and kill the two others! If they do draw, it’s against one and only one other dueller, and so, there is no possibility for collusion (as in: ‘Blondie, let’s get rid of this pig Angel!’ or ‘Tuco, you’re a good man, you should get some bucks out of Blondie’s corpse.’)

These conditions reduce the game to a basic form: which opponent each dueller is going to shoot? Payoffs are also pretty clear: the player either gets money or gets killed. Is there equilibrium here? In layman’s terms, is there a situation whereby duellers get the money and do not change their mind if they are offered to re-do the duel?

Clint Eastwood's rendition of Blondie was terrific. So was he in the other movies.

In fact, it seems there is. Not because the movie suggests so (as it later turns out, Blondie had Tuco’s pistol emptied the night before they reached the cemetery. In that sense, Blondie had a strictly dominant strategy of shooting Sentenza, which he did) but because the whole structure of the game incentive each dueller to implicitly coordinate with another to bring down the third: regardless of Blondie’s trick, both Blondie and Tuco fired –or tried to- on Angel. Why so, and was it equilibrium? If it was to be done again, would one of them at least change their mind?

Now, the game is imperfect: all three duellers have a history together. They know that of the three, Angel is the most ruthless and no one benefits from allying with him. On the other hand, Blondie and Tuco have a history of lucrative cooperation.

The table shows clearly that is it better to team up with with someone against the third dueller, rather than just draw and shoot at random (payoffs are sufficiently clear for them not to randomize. In gibberish economics, that means there’s already a Nash equilibrium, so randomizing is not necessary – the outcome of Nash equilibrium is obtained by mixed strategies). We need however, to introduce another condition: because all three protagonists dealt with each other before, they have preferences over their respective ‘partner’. It is reasonable to consider their preferences as follows:

For Tuco: U>G>B
For Blondie: G>U>B
For Sentenza: B>U>G

(note: duellers are considered selfish, so they prefer to take all the bounty to themselves, then choose another protagonist when needs to be) Because of that ordering, and even though pay-offs are the same when teaming-up occurs, both Blondie and Tuco have incentive to cooperate and shoot Sentenza, which eventually happened. In essence, there was little high-brow rationality, especially for Tuco: he is the exclusive second choice of both duellers, and he is better off with Blondie than he is with Sentenza -per his own preferences-.

Why does it constitute an equilibrium? Because it dominates all other moves, i.e. duellers -at least Blondie and Tuco- are better off and do not want to wish to change from their choices: Blondie prefers to split the money with Tuco, and so does the latter. Sentenza is know to be ruthless and has every incentive to keep it that way. It is thus a stable equilibrium.

Afrinomad put to me this proposal: can we find some Game Theory application to the current wave of revolutionary fervour in the MENA region? I must confess I got very enthusiastic over this idea: however intermediate my knowledge in game theory is, I’d very much like to give it a shot. So I would like to post on my own terms: ‘are the people of MENA ready to throw over their rulers, under Game Theory settings?’. Stay Tuned!