The Rules Behind the Vote: What Game Theory Reveals About European Elections - and Ukraine’s Democratic Future

This is where game theory becomes particularly useful for understanding political strategy.

An election is never simply a contest between isolated candidates. Every participant is making decisions while anticipating what others will do. Voters consider not only whom they prefer, but also who looks capable of winning. Parties decide whether to compete alone, form alliances or withdraw candidates. Campaign teams assess whether a new entrant will bring new voters or split an existing coalition. Political elites think not only about who is likely to win, but also about which coalitions could emerge afterwards.

In other words, elections are strategic games played within institutional rules. And those rules can shape the result just as much as campaign communication.

The same electorate can produce different winners under different voting systems.

Imagine three candidates. Candidate A receives 40 per cent of first preferences, Candidate B gets 35 per cent and Candidate C 25 per cent. Under a plurality system, A wins. But suppose most of C’s supporters prefer B to A. In a runoff, B could win instead. Under a ranked voting system, the outcome could change again.

The voters have not changed their political views. The mechanism used to turn those views into a result has changed.

For a political strategist, that distinction is fundamental. A rating cannot be interpreted separately from the electoral system. Thirty per cent in a single-round plurality election, 30 per cent in a two-round presidential contest and 30 per cent in a proportional parliamentary election represent three very different strategic positions.

European politics offers an especially useful field for this kind of analysis. The continent combines proportional systems, electoral thresholds, preferential voting, two-round presidential contests, coalition governments and elections to the European Parliament. Each system creates different incentives for candidates, parties and voters.

In a proportional system, for example, the electoral threshold is more than a legal barrier. It can also become a psychological one.

A party polling just below the threshold may have a loyal and committed electorate. But voters who believe the party will not make it into parliament may shift to a larger political force to avoid “wasting” their vote.

That shift can then reinforce the original expectation that the smaller party is not viable.

This is a coordination problem. Voters are not simply expressing their preferences. They are responding to what they believe other voters will do.

That is why campaign professionals should not look at a party polling at 4 or 5 per cent and focus only on the headline number. The more important questions are often elsewhere.

How loyal is this electorate? What is its second preference? Where will these voters go if they lose confidence in the party’s viability? Which larger political force benefits if the smaller party falls below the threshold?

A small party can therefore affect the distribution of political power even if it ultimately wins no seats.

The same logic applies to third candidates in majoritarian elections. A candidate does not have to win to determine who does.

Their strategic importance may depend on whose coalition they divide.

Suppose two leading candidates are close: one has 46 per cent and the other 44 per cent. A third candidate enters the race and receives 10 per cent, mainly from voters who would otherwise have backed the first candidate.

The third candidate remains far from victory, but changes the outcome.

In campaign practice, the relevant question is therefore not simply, “How much support does this candidate have?”

It is: “Which possible majority becomes impossible because this candidate remains in the race?”

In my own work with political campaigns, I have repeatedly seen that a candidate’s formal rating does not always reflect their real strategic weight.

A candidate with relatively limited support may control a decisive group of voters, influence who reaches a second round, prevent a majority from forming, or become essential to a post-election coalition.

Conversely, a candidate with a strong personal rating may have very little room to grow if most other voter groups find them unacceptable as a second choice.

This is why professional political research needs to go beyond standard voting-intention questions.

It should examine second preferences, negative ratings, transfer potential, coalition acceptability and how voters behave under different scenarios.

Who is the voter’s first choice?

Who is an acceptable second choice?

Against whom would the voter mobilise?

Would the voter stay home if their preferred candidate withdrew?

Would they vote strategically to prevent another candidate from winning?

These questions reveal the actual structure of the race.

The Condorcet paradox offers another useful insight. It shows that collective preferences can become circular even when every individual voter has a consistent ranking.

A majority may prefer A to B. Another majority may prefer B to C. At the same time, a majority may prefer C to A.

There is no single option that defeats every alternative.

For political practitioners, this is more than an academic curiosity. It helps explain why the way a political choice is framed can affect the result.

One campaign may define an election as a choice between stability and chaos. Another may frame it as reform versus the establishment. A third may present it as security versus weakness.

The candidates have not changed. The comparison has.

And when the comparison changes, the coalition capable of forming a majority can change with it.

This is the practical meaning of agenda control. Political power is not only about persuading voters. It is also about defining which alternatives are compared and the order in which they are presented.

The same principle applies in parliaments, party conventions, coalition negotiations and international institutions.

When several proposals are put to a vote one after another, the order can influence which option survives. An agenda setter can therefore affect the final decision without changing the underlying preferences of the participants.

Strategic voting is another unavoidable feature of elections with several viable alternatives.

The Gibbard–Satterthwaite theorem formalises an observation familiar to campaign professionals: under broad conditions, when voters choose between three or more alternatives, there will be situations in which a voter can benefit from misrepresenting their true preference.

In everyday political language, this is the vote for the “lesser evil”.

A voter may prefer Candidate C, believe that C cannot win, and vote for Candidate B to stop Candidate A from taking office.

That is not necessarily political inconsistency. It can be a rational response to the electoral system and the choices available.

For polling and campaign analysis, this means preference and intended behaviour need to be measured separately.

“Whom do you like most?” is not the same question as “For whom will you vote?”

And neither is enough without asking: “Under what circumstances would you change your decision?”

The perceived viability of a candidate is therefore a strategic resource.

Fundraising, endorsements, media coverage and polling do not simply reflect campaign strength. They can also create it.

Once voters begin to see a candidate as non-viable, support can collapse even when the candidate’s platform remains popular.

European coalition politics makes the picture even more complicated.

In parliamentary systems, an election does not always directly determine who will govern. Instead, it determines the political structure within which parties negotiate.

A party’s influence is therefore not necessarily proportional to its vote share.

A smaller party can become pivotal if neither major bloc can form a majority without it. Its bargaining power may exceed that of a larger party that has no realistic alternative coalition.

From a game-theory perspective, the key question is not simply how many seats a party controls.

It is how many viable coalitions require its participation.

This has direct consequences for campaign positioning.

A party may choose a more distinctive ideological message to mobilise its core supporters, or a more flexible profile to preserve future coalition options.

A candidate may attack a rival during the campaign while avoiding language that would make post-election negotiations impossible.

A party expecting to become a coalition broker will communicate differently from one seeking an outright majority.

This is also why European elections cannot be understood solely through a traditional left-right spectrum.

Contemporary coalitions can form around security, European integration, migration, economic policy, institutional trust or attitudes towards Russia and Ukraine.

Different issues create different possible majorities.

Ukraine will eventually face an even more difficult version of these strategic and institutional questions.

Future Ukrainian elections will take place in a society transformed by war, displacement, migration, military service, territorial disruption and profound changes in political identity.

The central challenge will not simply be organising a vote. It will be designing rules capable of producing legitimacy, representation and governability under exceptional conditions.

How should citizens living abroad participate?

How should internally displaced voters be represented?

How can military personnel vote without compromising security?

How should electoral districts reflect demographic changes caused by the war?

What threshold would preserve political pluralism without creating unmanageable fragmentation?

How should the electoral system address territories affected by occupation?

These are legal and constitutional questions. But they are also questions of mechanism design.

Every electoral rule creates incentives.

A threshold can encourage political consolidation, but it can also exclude significant groups. A purely proportional model can improve representation while increasing fragmentation. A majoritarian component may strengthen territorial accountability but become problematic when population patterns have been radically altered by war.

Remote or external voting can expand participation while creating new administrative and trust challenges.

There is no politically neutral solution. Nor is there a perfect electoral system.

Arrow’s impossibility theorem shows that no voting rule can satisfy every desirable democratic criterion at the same time when society has to choose between several alternatives.

In practical terms, electoral design is always a choice between competing values: representation, stability, accountability, simplicity, inclusiveness and resistance to manipulation.

For Ukraine, that means future electoral reform should not begin with the interests of individual political actors.

It should begin with a more basic strategic question: What behaviour should the system encourage, and which risks should it minimise?

Should the rules encourage party consolidation or ideological diversity?

Should they prioritise direct local representation or national proportionality?

How can the system prevent the exclusion of displaced citizens while maintaining public confidence in electoral administration?

What kind of coalition dynamics will the chosen system produce?

These questions should be modelled before the rules are adopted, rather than discovered after the election.

For political strategists, the broader lesson is straightforward.

Electoral analysis cannot stop at ratings. It has to examine the architecture of the contest: the voting system, thresholds, the sequence of rounds, second preferences, coalition potential, negative mobilisation and voters’ strategic expectations.

A campaign is not simply a race for the highest number.

It is an attempt to build a winning majority under a specific set of rules.

Sometimes that majority is built through persuasion. Sometimes through turnout. Sometimes through the transfer of votes between rounds. Sometimes through the collapse of a competitor below an electoral threshold.

And sometimes the decisive result emerges only after election day, at the coalition table.

Game theory does not replace political judgment, sociology or field experience. It makes them more precise.

It helps explain why a seemingly strong candidate can be structurally weak, why a small political actor can become decisive and why changing the rules can change not only the result, but the behaviour of every participant.

Elections do not simply reveal public preferences.

They organise them, filter them and convert them into political power.

That is why the rules are never merely technical.

They are part of the political strategy itself.

WRITTEN BY: Kateryna Odarchenko