The game theory of Scottish independence

Scottish independence is normally discussed as if it were primarily an argument about persuasion: we need to persuade more people, build a stronger mandate, demonstrate that independence is economically viable, win more elections, organise bigger marches and perhaps reach a point where support for independence is consistently above 50, 55 or even 60 per cent, after which Westminster will somehow find itself unable to continue saying no.

I’m increasingly convinced that this is the wrong way to look at the problem, because the fundamental question is not whether Scotland can demonstrate that it deserves another independence referendum, but whether Westminster has any reason to grant one, and that is less a question of morality or democratic legitimacy than of incentives, bargaining power and, ultimately, game theory.

Imagine that Westminster has two choices: it can grant Scotland another recognised independence referendum, or it can refuse one. If it grants one, there is some probability that Yes will win and Scotland will leave the United Kingdom, which from Westminster’s point of view represents a potentially very large loss, both materially and symbolically; and even if No wins, Westminster will still have reaffirmed the principle that Scotland can reconsider its membership of the UK whenever political circumstances appear to justify another referendum, which is hardly an attractive precedent if your objective is to preserve the Union.

If Westminster refuses, however, the consequences are much less alarming. Scottish politicians complain, the SNP wins elections, the Scottish Parliament passes motions, people march through Glasgow and Edinburgh and social media fills with indignation, but HMRC still collects Scottish taxes on Monday morning, Scottish MPs continue sitting at Westminster, Scottish authorities continue administering the law and Scotland continues functioning perfectly normally as part of the United Kingdom.

Seen from London, therefore, this is not a particularly difficult calculation, because granting a referendum carries the risk of losing Scotland whereas refusing one has so far carried little more than the risk of another angry speech, another march and another round of accusations that Westminster is ignoring Scotland’s democratic wishes.

In game-theoretical terms, the independence movement has helped create a game in which refusal is an extremely attractive strategy, and this is why I have never been persuaded by the idea that Scotland can simply accumulate enough democratic mandates until Westminster eventually has to give in, because there is no constitutional deity sitting above the two sides, patiently counting election victories and awarding a referendum when Scotland has collected the required number. Westminster is not the referee in this game but one of the players, and players respond to incentives.

A very simplified version of Westminster’s calculation is therefore that if it grants a referendum and No wins, the cost is tolerable; if it grants one and Yes wins, the cost is enormous; if it refuses and Scotland accepts the refusal, the cost is tiny; and if it refuses and Scotland somehow makes continued refusal seriously troublesome, then the cost may eventually become substantial. At the moment we are overwhelmingly in the third situation, which means that the strategic problem for the independence movement is not primarily how to strengthen the mandate, but how to change the payoff structure so that Westminster eventually finds refusal more troublesome than agreement.

Put more simply, Westminster will not grant Scotland another referendum because Scotland deserves one; it will do so when refusing one becomes the worse option.

This might sound cynical, but it is how political bargaining normally works, and the history of devolution is a useful illustration because it is often remembered as a story about Scotland patiently developing an overwhelming democratic consensus between the failed referendum of 1979 and the successful one in 1997, whereas the more important point is that powerful actors within the British political system wanted devolution too.

Labour wanted it, the Liberal Democrats wanted it, much of Scottish civic society wanted it and large parts of the Scottish media wanted it, while Labour in particular could see obvious advantages in creating a Scottish Parliament, both as a response to long periods of Conservative government from Westminster and as a means of containing the SNP. Devolution therefore had something independence currently lacks: a coalition containing players who actually possessed power within the British state and who believed constitutional change was in their own interest.

When Labour won the 1997 general election, it did not reluctantly concede a Scottish Parliament because Scotland’s pile of democratic mandates had finally reached some irresistible height; it implemented a policy it supported, which is a rather different thing.

This is a fairly standard bargaining problem, because if you want another player to agree to something, it helps enormously if the agreement gives them something they want, and it is worth asking what the equivalent offer is today. Why should a Labour Prime Minister grant an independence referendum, or a Conservative one, or Reform, or the Liberal Democrats? There are perfectly respectable moral arguments about democracy and self-determination, but political parties are not moral philosophers: they seek office, power, votes and the successful implementation of their programmes, and being remembered as the Prime Minister who lost Scotland does not obviously advance any of these objectives.

Another useful concept from game theory is the outside option, meaning what happens to each player if no agreement is reached. Suppose I want to buy your house: if you desperately need to sell tomorrow and I am the only potential buyer, I have an excellent bargaining position, whereas if you are perfectly happy to stay there for another twenty years while three other buyers are competing with me, yours is much stronger. The important point is not simply how much either of us wants the deal, but what happens if there is no deal.

Westminster currently has an excellent outside option in negotiations over Scottish independence, because it can simply say no, whereas Scotland’s outside option is considerably worse, because if Westminster refuses a referendum, Scotland remains in the United Kingdom.

That asymmetry explains an enormous amount, and it also helps explain why repeatedly demonstrating a mandate might not have the cumulative effect that gradualists often imagine, because Scottish politics is not a one-shot game but a repeated one in which both sides learn from previous rounds. Every time Scotland elects another pro-independence majority, demands another referendum, is refused one and then carries on much as before, Westminster acquires useful information: it learns that refusal is cheap.

This may in fact be almost the opposite of the gradualist assumption, because another ignored mandate does not necessarily move Scotland one step closer to independence; it may instead reinforce Westminster’s belief that Scottish mandates can safely be ignored, particularly if each new confrontation ends in much the same way as the last.

Repeated games also depend heavily on credible threats, because if one player says, “If you refuse our demand, there will be consequences,” and nothing happens when the demand is refused, the threat becomes weaker the next time, and after enough repetitions the opponent quite rationally begins to discount it almost entirely. Scotland has spent much of the period since 2014 demonstrating that refusal will be met with indignation, but not necessarily with consequences, which is a poor way of increasing bargaining power.

This does not mean that the answer is violence, riots or making Scotland ungovernable simply for the sake of it; apart from the moral objections, actions that mainly hurt Scots would be strategically idiotic. Unfortunately, however, this is precisely where Scotland has a rather peculiar structural problem, because many traditional forms of civil resistance are badly targeted in a devolved state.

If people refuse to pay council tax, they damage Scottish councils rather than Westminster; if they disrupt schools or hospitals, they damage services controlled from Edinburgh; if they boycott ScotRail, they hurt a Scottish public service; and much of the taxation that actually matters to Westminster is collected directly by HMRC, often through employers before the individual taxpayer ever sees the money. Scotland therefore has many institutions that look remarkably state-like, but relatively few levers that can directly impose costs on the British state, which makes the strategic problem unusually difficult.

The ideal form of pressure would have three properties: it would impose a substantial cost on Westminster, impose very little cost on Scotland and retain broad democratic legitimacy. Most obvious tactics fail at least one of these tests, because marches have enormous legitimacy and very little cost to Scotland but can easily be ignored by Westminster, while disrupting Scottish public services may create plenty of noise but mainly harms Scotland, and illegal tax resistance might impose more direct costs but would expose individuals to serious penalties and could rapidly lose public support.

The independence movement therefore needs to think much more seriously about the relationship between cost to Westminster, cost to Scotland and public legitimacy, rather than simply counting how many people attended the latest march or how many mandates have now been accumulated.

There is also a coordination problem, because the independence movement is not one player but many, and the SNP, the Greens, unaffiliated campaigners, civic organisations, bloggers, local groups and individual voters do not all have identical interests. Political parties may want independence, but they also want seats, ministerial offices, favourable media coverage and successful election campaigns; individual politicians have careers, organisations want members and donations and activists disagree, often ferociously, about tactics.

This creates what game theorists call a collective-action problem, because everybody might benefit if the movement adopted a coherent strategy that gradually increased the cost of Westminster’s refusal, while every individual organisation has an incentive to avoid risky actions and allow somebody else to carry the burden. In other words, everybody benefits from pressure, but everybody would quite like somebody else to apply it.

There is also a coordination problem over escalation, because if ten organisations independently invent ten different ways of “putting pressure on Westminster”, the likely result is not pressure but noise: one group organises a march, another launches a boycott, a third starts a petition and a fourth announces that the next election will be a de facto referendum, while Westminster quite reasonably concludes that it can wait for the excitement to pass.

Effective pressure normally requires the opponent to know what happens next if the current tactic fails, which is one reason I have previously argued for a non-party independence organisation built around a common strategy but organised in a decentralised way, not because Scotland needs some romantic revolutionary underground, but because political parties are poorly suited to running a sustained campaign of constitutional pressure when they have so many other interests and so many reasons to avoid frightening marginal voters.

Such a movement could establish something resembling an escalation ladder, where Westminster would know that if it ignored A, the movement would proceed to B, and if it ignored B, it would proceed to C, with each stage remaining peaceful, democratic and proportionate but with the crucial difference that refusal would produce predictable consequences rather than yet another reset to the status quo.

That matters because politics is not only about present costs but also about expected future costs, and Westminster does not need to find Scotland intolerable today if it comes to believe that continuing to refuse a democratic route will become progressively more troublesome in future. Once that expectation changes, the payoff structure begins to change with it.

There is, however, another possibility, and I increasingly suspect it may be the more likely one, namely that the game itself changes before Scotland ever succeeds in changing Westminster’s incentives from within the existing constitutional arrangement.

Irish reunification is the most obvious mechanism, because Northern Ireland differs fundamentally from Scotland in that its constitutional position already contains a recognised route out of the United Kingdom, so if support for reunification eventually becomes sufficient to trigger a border poll and Northern Ireland votes to join the Republic, Westminster cannot simply deploy the Scottish strategy of saying no indefinitely.

The consequences for Scotland could be profound, because the idea that the United Kingdom is permanent would disappear overnight once one of its four constituent parts had left through a recognised democratic mechanism, while the strategic calculations inside England might also begin to change as the question ceased to be how an ancient four-nation state could be preserved and became instead what kind of state England, Scotland and Wales wished to inhabit after Northern Ireland had gone.

At that point Scottish demands for another referendum might cease to look like an existential attack on the United Kingdom and start looking like one element of a wider constitutional reconstruction, and it is not impossible to imagine pressure emerging for simultaneous constitutional votes throughout the country, with Northern Ireland choosing between the UK and Ireland, Scotland deciding whether to remain in the residual union or become independent, Wales reconsidering its own position and England finally, astonishingly, being asked what constitutional arrangement it actually wants.

That would transform the Scottish game completely, because Scotland would no longer be a supplicant asking Westminster for permission to leave an apparently permanent United Kingdom, but one of several players deciding what should succeed a constitutional arrangement that was already changing, and once that happens the available strategies, the relevant coalitions and the payoffs attached to each possible outcome all change at the same time.

Game theory is not deterministic in the sense of locking players forever into a fixed matrix, because players can change, preferences can change, coalitions can form and entirely new strategies can suddenly become available, but relying on some external constitutional shock to reorganise the game in Scotland’s favour is not much of a strategy in itself.

For the moment, therefore, the fundamental problem remains that Westminster has discovered it can refuse another independence referendum at very low cost, while the independence movement has responded mainly by trying to demonstrate ever more convincingly that Westminster ought not refuse one, which means that Scotland is still making an argument about legitimacy while Westminster is making a calculation about incentives, and until the independence movement finds a way either to change those incentives or to exploit some wider change that alters them on its behalf, it should not be terribly surprising that the side with the better outside option continues to win.