Game theory — and Scottish independence — Alex MacMillan:

A brief excursus from the law to tackle current affairs…

Following the electoral results from Saturday (8 May 2021), the Financial Times reports today that Michael Gove, UK Cabinet Office Minister, has waved aside the suggestion that an advisory referendum on independence is on the cards — Westminster’s ‘exclusive attention’ is on the nation’s recovery from the pandemic. And Douglas Ross, the leader of the Scottish Conservatives, points to the failure of the SNP to achieve an outright majority — there is in consequence no democratic mandate for a rerun of the previous 2014 independence referendum, he says (outcome: 45% to 55% in favour of the Union).

Unfortunately for Mr Ross, his argument omits to consider the role of the Green Party — which also committed to a referendum in its manifesto. The SNP came very close indeed to an outright majority; and putting the SNP vote together with the Green vote, there unmistakably is a democratic mandate for a further referendum (if, adopting his reasoning, that is how mandates are properly deemed to exist).

The loss of Scotland from from the UK would be a catastrophic legacy for this Government, which is a government of (to give it its full title) the Conservative and Unionist Party. And it would be particularly painful for PM Boris Johnson, since there is a fairly neat analogy between the arguments he mobilised in favour of Brexit and the arguments he would have to try and bat away.

What strategic choices lie open to this pro-Union Government? The SNP have made the first move in this sequential game by calling for a referendum. The ball is now in the PM’s side of the court. What is the best response to the SNP’s calls for an advisory referendum? Simplifying slightly, there are only three possible stances for the Prime Minister:

  1. Oppose the referendum outright;
  2. Accede to the referendum; or
  3. Delay.

Going through these in turn, from the Government’s perspective (and using ordinal numbers to express levels of preference) the payoffs are as follows:

  1. Oppose ~ 1. The Government pleases its political base by supporting the union, but risks antagonising the Scots;
  2. Accede ~ -2. The Government would be seen as failing to uphold its commitment to the Union and would set in train a risk of the breakup of the UK.
  3. Delay ~ 2. The Government avoids the politically and constitutionally dangerous territory of Scottish independence, hopefully until the political landscape has shifted in its favour.

Turning the tables, we also need to consider the SNP’s perspective. What are its payoffs in respect to these three Government strategies? Well, clearly its payoffs depend on how it chooses to act. But these are the guiding considerations, I suggest:

  1. Oppose. The SNP can rely on this as evidence of Westminster’s oppressive conduct, and can litigate with a reasonable chance of winning on this point of constitutional law, which the Supreme Court would have to rule on.
  2. Accede. The SNP have a second bite at the cherry with a referendum; given the fallout from Brexit (a constitutional decision taken without the democratic assent of the people of Scotland) there is a reasonable chance that the outcome of a second referendum would favour independence — but it would without doubt be a close-run thing.
  3. Delay. The SNP can accuse Westminster of frustrating Scotland’s mandate, and may try and take steps to arrange an advisory referendum in any event, which may lead on to scenario 1 above. But there is some risk that the political landscape will shift and the optimum moment for a referendum may pass.

And the SNP/Holyrood’s strategy set contains three strategies:

-Proceed with a referendum with or without Westminster’s blessing;

-Litigate to try and establish the right to hold a referendum;

-Wait to see if the political landscape changes to favour allowing a referendum.

Plotting the above, and giving the SNP the response strategy set of Proceed — Litigate — Wait as an answer to Westminster’s Oppose — Accede — Delay strategy set, the normal form strategy matrix looks like this:

The stars indicate the three Nash equilibria that exist for this strategic game (ie mark the scenarios in which neither party has an incentive to change strategy, if the other player’s strategy remains unchanged); the arrows represent the best response moves. I will say a little bit more about these annotations below.

Nash equilibria do not necessarily represent optimal outcomes for all parties. The Prisoner’s Dilemma is one of the classic examples where the Nash equilibrium predicts a sub-optimal outcome, the latter being an example of parties’ best mutual responses leading to an outcome that is inferior, and illustrating the potential for players’ apparently rational choices to lead to undesirable outcomes.

To explain one Nash equilibrium from the matrix above, my assumption is that, given Westminster’s choice to oppose a referendum, Holyrood would suffer a loss if it chose to do anything other than proceed (litigate and the SNP might lose; wait and the chance slips away); and equally if the SNP are intent on proceeding with an advisory referendum, Westminster would suffer a loss if they did anything other than oppose that referendum by attacking its legitimacy/legality. So the top left-hand strategic pairing represents one equilibrium state.

The arrows indicate the players’ motivations to change strategy to avoid loss. For the SNP, for example, the strategy of waiting for a referendum to be allowed is highly unsatisfactory and will always lead to a shift to a more aggressive strategy in order to achieve a higher payoff.

Our game theory matrix predicts that, assuming my assessment of the strategic options and order of preferences is right, the Scottish referendum issue will not be wished away by the Conservative government, although ‘delay’ remains their best strategy at present.

Assuming Westminster’s present strategy is to delay addressing the question, the matter will either be resolved in the courts or Holyrood will proceed with an advisory referendum without Westminster’s approval (which would also be challenged in the courts). Either way, the Prime Minister has a substantial constitutional headache that is most unlikely to recede in the coming months.

And… Game theory in the context of legal advice

I touch on a practical application of Game Theory because I wanted to illustrate that the same approaches used in political analysis can also be helpful in litigation and settlement. Where helpful and relevant, I try and incorporate game theoretical analysis into my legal advices: its main advantage lies in forcing the advisor to rise above a single party’s interests and imagine the stakes for the other side. An aim of litigation should not merely be to establish the strengths of your own case, but also to gather information about the other side’s likely payoffs. Because by better understanding those payoffs, you can anticipate the future course of the litigation and establish the other side’s ‘pain threshold’ in settlement discussions — being the point at which their interests are better served by proceeding to court in lieu of pursuing settlement.

Originally published at http://www.alexmacmillan.co.uk on May 10, 2021.