What can game theory teach us about Repselect?

Because student politics is just a game.

Hack Christmas is upon us. Today is Repselect, where the Students’ Representative Council (SRC) will meet to decide the Office Bearers (OBs) who will run the SRC in 2022.

Repselect is the crown jewel of stupol chicanery at USyd, generating a litany of infamous and legendary moments. It’s the culmination of weeks of delicate negotiations between an eye-watering 12 factions on next year’s Council.

Because of the very scattered nature of this year’s SRC results, a clear majority (20 out of 39 Councillors) is almost impossible. Instead, student politicians must assemble a motley crew of power-hungry factions to get their nominees elected. Compromises must be made, and betrayals are rife.

Engineers, Penta and Phoenix are looking like the kingmakers, but not even Councillors, let alone pundits, can know for sure what will happen tomorrow night.

But luckily, my third-year Economics unit can shed some light on these backroom deals – through a branch of game theory called “coalitional theory,” pioneered by economists John von Neumann and Oskar Morgenstern. If players (factions) play a game (stupol) where they have to form coalitions to win, and the payoffs of the game (different deals between factions for OB positions) are known, game theory can tell us what coalitions might stick and who might get different positions. I must disclaim that these are not strict predictions, but merely illustrations of what could hypothetically happen tonight.

Observation 1. The relative strength of each player matters

Building a coalition is all about bargaining power. The more Councillors your faction has, the more power you have to pick and choose your coalition partners, and to discard factions that don’t align with your interests.

Grassroots and Switch (the shell company for Grassroots) have 10 Councillors. Unity (Labor Right, including Horsegirls 4 SRC), together with Ignite (a Conservatorium-based faction which supported Unity’s Matt Carter for President), also hold 10.

These two groupings, as expected have led opposing coalitions. Grassroots has Pump (Labor Left), Socialist Alternative and Solidarity; while Unity has Ignite, Wave, Strive (Moderate Liberals) and Colleges for SRC. While Grassroots previously failed in trying to bring Unity over, there’s always the eventual possibility of a left-wing “supermajority,” an almost-impenetrable coalition made up of most factions. 2019 and 2020 both saw supermajorities prevail, locking out the Liberals from key OB positions.

Ordered roughly from left-wing to right-wing, the 2022 Council is made up of:

  • Socialist Alternative: 1 seat
  • StrikeBack (Solidarity): 1 seat
  • Grassroots/Switch: 10 seats
  • Pump: 1 seat
  • Engineers: 3 seats
  • Penta: 5 seats
  • Phoenix: 2 seats
  • Unity + Horsegirls: 6 seats
  • Ignite: 4 seats
  • Wave: 2 seats
  • Strive: 2 seats
  • Colleges: 2 seats

Observation 2. For coalitions to work, they must be stable

Every single successful coalition must be “stable” (in the “core” of the game), meaning that no player (or sub-coalition) can defect to another coalition to get a better outcome.

In practice, it means that coalitions must convince possible defectors to stay on their side. Left-wing supermajorities tend to be surprisingly stable, as there’s often nowhere else left to go if you defect, and they’re often strongly bonded over the desire to lock conservatives out. If the left can’t corral a supermajority together, the swing votes will be Engineers (3 seats) and international student factions Penta (5 seats) and Phoenix (2 seats).

Few would have predicted that Engineers, a recently-established faction with a specific demographic appeal, would have held the balance of power. They’ve been courted by both Grassroots (current President Swapnik Sanagavarapu and incoming President Lauren Lancaster) and Unity (factional heavyweight Angelina Gu), promising them General Executive positions.

Engineers have historically worked with Grassroots on Council, and are leaning towards Grassroots to support stable coalitions and ensure that the President has favourable OBs to carry out their mandate. However, they are open to exploring things with Unity, not least because they have been occasionally put off by Grassroots’ behaviour on social media.

Penta is a remnant of the Panda faction, which has been successful at heavily mobilising international students. Penta supported Lancaster for President. Meanwhile, Phoenix originally supported Carter, but surreptitiously changed their support in the final days of the election to Lancaster. Watch their loyalties.

Observation 3. Coalitions should allocate the biggest payoffs to pivotal players

If your coalition wins, you need to decide how you will divide up the payoffs (the OB positions). Understanding this step will help keep your coalition stable.

In economics, there’s a concept called the “Shapley value,” which tells us the payoff each player in a coalition should get, so that the eventual allocation is fair to everyone. The Shapley value says that a player’s payoff should be based on their power in making the coalition – in essence, the proportion of times they are “pivotal” to the outcome (a coalition that includes them wins, but a coalition that excludes them loses). 

With 5 seats in the middle, Penta is the most pivotal faction, and therefore should theoretically be offered a greater share of OB positions, such as General Secretary (one position going to Alana Ramshaw under the Grassroots deal). However, there have been rumblings of Grassroots promising Engineers extra General Executive positions (alongside their own nominees Tiger Perkins, Ashrika Paruthi and Eamonn Murphy), which would turf out Penta. It’s a dangerous move which risks Penta defecting to Unity.

It’s also important to understand who won’t defect, no matter how the cookie crumbles. After their initial offer, Grassroots promised Engineers ½ of an Education Officer (and also toyed with giving it to Solidarity), which has historically been reserved for SAlt. It’s unclear if this offer still stands, but nevertheless, there’s no way SAlt will defect to a bloc including Liberals.

On the Unity side, the payoffs would be distributed amongst Wave, with one Vice-President (likely SULS Presidential candidate Ben Hines, which would be unheard of for a brand-new faction with only two seats); Unity, with two General Secretaries; and the Moderate Liberals, with two General Executives. It’s unknown how Engineers, Penta and Phoenix factor into this equation.

However, tensions between USyd Unity and the national branch of Unity actually bode poorly for the Liberals’ chances. The Liberals have previously traded any elected National Union of Students (NUS) delegates to Unity, in exchange for being included in Unity’s Repselect deals. However, USyd Unity this year doesn’t care as much about supporting the national branch, meaning that the Liberals don’t have that same bargaining chip.

Observation 4. Sometimes, game theory is just a theory

In actuality, real life imposes constraints on game theory’s predictions. For example, game theory cannot easily capture the political leanings of players, such as which coalitions are simply unworkable due to political differences.

The model also only works under perfect information – that is, where all the possible deals for each possible coalition are clearly outlined. Factions in the middle, like Engineers, probably have near-perfect information, as it’s not in anybody’s interests to lie to them. However, there’s “information asymmetry” for all other players – they know the deals they’ve made, but can’t know what their opponents said to others. And it might even be in their best interests to spread misleading information, which could destroy the model.

And for all this to work, we must assume that players are rational and logical, making decisions based on their own self-interest and not out of emotion, impulse or pre-existing friendships. Maybe that’s where it all falls down. Famously, rational behaviour is not a strong point of Repselect. Tonight will test whether the cold, hard logic of game theory can match up against the insane beast that is USyd student politics.