Do we let Game Theory dictate our lives?

We relinquish control over aspects of our daily lives to the government we elect. The behaviour of this government can be understood through game theory, where political parties act as players, making strategic decisions based on expected payoffs and outcomes, often converging toward a Nash equilibrium.

Game theory overview

The most well-known example of game theory is the Prisoner's dilemma. It involves two individuals who have committed a crime and are questioned separately. Each has two choices: cooperate by staying silent, or defect by betraying the other. If both remain silent, they receive a moderate sentence. If one betrays while the other stays silent, the betrayer goes free while the other receives the maximum sentence. However, if both betray each other, they both receive a harsh sentence.

Although mutual cooperation leads to a better overall outcome, each individual has an incentive to betray in order to minimise their own punishment. As a result, both prisoners act in their own self-interest and end up worse off, demonstrating how rational decisions at an individual level can lead to inefficient outcomes collectively. This logic can be applied to modern Parliament. More specifically the divide between Labour and Conservatives.

The origins of party strategy: Early ideology and political positionings

The Conservative party, born in the 1830s, were originally right-wing. Emphasising land ownership rights, free markets, individual liberty, slight reformation but not major change, upholding tradition; the monarchy, how the government is ruled and the Church of England.

The Labour party, born in 1900, were originally left-wing. Emphasising the representation of the working class in government, public welfare, common ownership, nationalisation, democratic socialism, adopting a more radical approach.

Current party strategy

Currently, most people would see Labour and the Conservatives as two sides of the same coin. This is due to significant changes in their policies and core beliefs. The Conservatives now emphasise the reduction of government spending, low income tax, reduction of welfare, increasing housing subsidies, improving the NHS workforce, apprenticeship funding and improving schools. Labour now emphasises the improvement of the NHS, funding more state education, increasing the minimum wage, and fiscal responsibility.

Current strategies of the Conservative and Labour parties reflect decades of strategic adaptation to public opinion. While today their policies may seem similar, this convergence is the result of lessons learned from historical election outcomes.

Post-war general elections

1945 - Labour majority
1955 - Conservative majority
1959 - Conservative majority
1964 - Labour majority
1966 - Labour majority
1970 - Conservative majority
1974 (Feb) - Labour minority
1974 (Oct) - Labour majority
1979 - Conservative majority (Thatcher)
1983 - Conservative landslide (Thatcher)
1987 - Conservative landslide (Thatcher)
1992 - Conservative majority
1997 - Labour landslide (Tony Blair)
2001 - Labour landslide (Tony Blair)
2005 - Labour majority (Tony Blair)
2010 - Conservative minority
2015 - Conservative majority
2017 - Conservative minority
2024 - Labour landslide

How changes in public opinion shape policy

From 1945, both the Labour and the Conservative parties began adjusting policies and promoting their successes in order to sway the general public and their patrons into voting.

In the October 1974 election, Labour claimed that it ended the Miner's strikes, gaining tremendous popularity among the public, contributing to their majority win. A development that was not anticipated by the Conservatives. Following the perceived failure of implementing ideas of democratic socialism (1974–77) in the forms of planning agreements and nationalised car companies (British Leyland), the British public shifted its preferences. Recognising this shift, Thatcher capitalised on the opportunity, aligning Conservative policies with voter sentiment, thereby creating and solidifying her dominance in British politics. Her policies can be explained in one quote:

"At its most crude, Thatcherism represents a belief in free markets and a small state. Rather than planning and regulating business and people's lives, the government's job is to get out of the way."

However, her reluctance to deviate in favour of the public in comparison to other candidates led to her reign being cut short. The most notorious example of her strategy failure is the introduction of the poll tax, a flat tax paid by everyone to their local authority, leading to riots breaking out. Once again, the public shifted its ideas. Anticipating the change in opinion, Blair took advantage of the situation, securing him a landslide victory.

After the 2008/9 financial crisis, public opinion shifted once more, distrust in the government was rising, leading to a minority Conservative government. After 2008/9, the logic of the "crisis happened, leading to a shift in opinion" model does not hold. For the 2015 election, voters chose parties based primarily on strategy. The Conservatives put forward a new idea: Brexit. This new idea was attractive enough for voters to swing towards the Conservatives in the election, and helped gain a majority vote.

From 2017 to 2024, the government became increasingly unpopular due to their activities during the Covid lockdown, the backlash of Brexit, foreign policy such as the war in Ukraine and poor governing including Liz Truss admitting to have not done what she was elected to do. Amidst all the large resentment towards the Conservatives, Rishi Sunak anticipated the change in opinion, leading to his new Mandatory Service pledge, trying to recover any lost votes. However, this attempt was futile as Starmer gained significant popularity among the public with his campaign highlighting the need for "Change", securing him a landslide victory.

Throughout recent history, there have been numerous changes in the government, with policies changing every election. These policies began to converge towards a common set, an equilibrium. This is represented through the Nash equilibrium, where each party has no incentive to deviate, as their policies maximise voter support.

Summary of the model

Each party has a voter base, this voter base is modelled as a basket. The voters will be modelled as rocks with the ability to roll into their preferred player's basket. The player with the most rocks by the end of each round gains control of the rules of the game and can announce the end of each round. Each player aims to successfully anticipate what the other players will do and the changes of the game's environment in order to win each round.

Before 1900, the major player of this game was the Conservative party, they controlled all the rocks, what each rock was allowed to do, what they were allowed to own. After 1900, a new major player joined: Labour. Each player changed their strategy of attracting rocks, until a common strategy was found between the two major players.

At first, the government is understood to act in the best interests of the country, prioritising what is right for society both now and in the future. However, this ideal becomes strained as political competition intensifies, and players begin to behave more strategically. Each player then starts to deviate, adjusting their approach in pursuit of the electoral payoff offered by voters. They did this by adjusting policies, such as Rishi Sunak's mandatory public service pledge, Keir Starmer's online safety act, Thatcher's Thatcherism, and Tony Blair's minimum wage, all of which carried the potential for significant negative outcomes when implemented, much like the Prisoner's dilemma. However, as the dilemma illustrates, the prospect of avoiding these negative consequences and achieving a more favourable individual outcome often incentivises players to take the risk regardless.

Application of the model to our daily lives

We give the party we vote for the responsibility of dictating how much of our incomes they take, what bins we have to put our waste in, what food we are allowed to eat, what drinks we are allowed to drink, what games we are allowed to play, what we can say, what we can view, what we can wear, what we can believe at times, etc. We let our daily lives be bound by those we put in power, and those who we put in power are bound by the logic of the prisoners, the logic of game theory. Therefore, by empowering political actors who operate under strategic incentives, we indirectly allow game theory to shape the structure of our daily lives.

Bibliography

Tamworth Manifesto - https://www.britannica.com/topic/Tamworth-Manifesto

1900 Labour Party General Election Manifesto - http://www.labour-party.org.uk/manifestos/1900/1900-labour-manifesto.shtml

Conservative Manifesto 2024 General Election - https://public.conservatives.com/publicweb/GE2024/Accessible-Manifesto/Accessible-PDF-Conservative-Manifesto-2024.pdf

Labour Party General Election Manifesto 2024 - https://labour.org.uk/wp-content/uploads/2024/06/Labour-Party-manifesto-2024.pdf

List of General Elections - https://researchbriefings.files.parliament.uk/documents/CBP-7529/CBP-7529.pdf

British Leyland - https://www.britannica.com/money/British-Leyland-Motor-Corporation-Ltd

Thatcherism - https://www.bbc.co.uk/news/uk-politics-22079683

Liz Truss "Didn't do what she was elected to do" - https://www.bbc.co.uk/news/uk-62750866