Striking a balance: how to win over new voters without losing the traditional base

How can a political figure attract new voters whilst preserving their existing electoral base? Drawing on the theory of location games, economics researcher Gaëtan Fournier and engineer Amaury Francou explain how politicians can choose a new strategic position, and bear the consequences of this change.

Although Emmanuel Macron originally presented as a centrist candidate in 2017, he has since adopted a more conservative stance on certain issues, such as security and immigration in the presidential election campaign in 2022. This ideological shift is evidence of the President’s strategy to attract right-wing voters while at the same time hoping to retain the support of centrists through his social and economic accomplishments. The manoeuvre is intended to fulfil two objectives: neutralise the threat posed by right-wing and far-right candidates, and broaden his appeal across the political spectrum. But is it actually possible for Macron to achieve this without alienating his electoral base?

In their article ‘Location Games with References’, published in the scientific journal Games and Economic Behavior in 2023, economics researcher Gaëtan Fournier and engineer Amaury Francou use location theory, a sub-field of game theory, to explain how political parties and companies can choose to occupy strategic positions - both ideological and geographical - while assuming the costs when they deviate from a reference location.

The rationality of political choice

Game theory, theorised by mathematician John von Neumann and economist Oskar Morgenstern in their 1944 book Theory of Games and Economic Behavior, makes it possible to analyse and model the strategic behaviour of ‘players’ - individuals, parties, companies, etc. - in a variety of contexts. Via its numerous applications, game theory is used in a range of fields, from biology and geopolitics to sociology and computer science.

 The Nash equilibrium, a key concept, occurs when no player can improve his situation by changing his strategy, if the others maintain theirs. In politics, the equilibrium can be interpreted as a theoretical prediction of possible alliances or compromises between parties. The American political scientist William H. Riker explored this topic in his book The Theory of Political Coalitions, published in 1962.

The work of the two researchers is underpinned by two main principles. The first is Hotelling's theory of minimal differentiation, where commercial agents endeavour to reduce the differences between their offerings, assuring homogeneity in the market. The political application of this is known as the median voter theorem. 

To understand this, we need to imagine an economic line along which voters' political opinions run from the left to right. The median voter is located such that there are as many voters to the left as to the right. The criteria can also be modified by differentiating, for example, between libertarian and authoritarian policies.

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The second principle is the economic theory of rational choice, which attributes rational behaviour to all stakeholders, with a preference for seeking the maximum profit for the lowest possible cost. According to the economist Anthony Downs - who has applied this latter principle to political democracy - this means that political parties act in such a way as to maximise their electoral success by adopting opportunistic policy proposals to appeal to voters. In other words, they will say anything to win an election. According to this theory, political parties are motivated solely by the desire to gain power rather than by deep ideological or political considerations. In a two-candidate election, therefore, they will tend to position themselves in proximity to the median voter.

On this point, however, Gaëtan Fournier and Amaury Francou deny that parties are motivated only by election victory, but argue that they are also driven by their political convictions. To demonstrate this, they draw on the work of economist and political scientist John Roemer. Roemer believes that political parties have ‘militant’ motivations, and tend not to go against policies that represent their party ideology.

Standing firm: achieving balance without losing the base

The study assumes that candidates are both opportunist and ‘militant’. They must therefore reconcile two objectives: maximising their share of the vote, while minimising the distance between their true convictions and their voter base. This demonstrates that it is possible to propose reforms that move away from the ideological core - from what the voter base considers to be the essence of the party - up to a certain point, beyond which the marginal gain in new voters is insufficient to compensate for the loss of members of the faithful electorate. Disparities in the Nash equilibria are introduced as a function of the strength of the anchoring effect, i.e. loyalty to a party's political ideology, taking into account the strategic interactions between politicians and voters.

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Staying loyal to well-known products to reassure consumers

The resulting theory is completely applicable to other fields. In industry, for example, in a competitive market such as that for technological products, companies have to choose where to place their products (in terms of technical characteristics, price, and so on) in order to maximise their market share, while taking into account the costs involved in differentiating their products from the existing standard or benchmark. A technological innovation, however ‘disruptive’ it may be, could appear to be a valuable way of winning market share, but the addition of the costs inherent to introducing a new product may undermine consumer satisfaction.

Ultimately, the approach taken in this study enriches our understanding of electoral dynamics and market strategies by taking account of costs that may be incurred when deviating from ideological positions of reference. It provides a better understanding of why the most extreme candidates to an election remain faithful to their ideologies despite the apparent advantages of moving towards the center. Similarly, it helps to understand why some companies may remain committed to their benchmark products in the face of market pressures.