Parties and seats
Who wins the votes that the government loses, and how these votes become seats. This page covers equations E19, E20 and E21.
In plain words
Each country has its parties, and each one is placed on twelve sliders, from 0 to 100, which say what it thinks about the economy, society, the world and power (E19). On election day, the incumbent camp wins or loses votes depending on the economy, as E15 says. When it loses votes, its partners lose more than the party that leads it, and these votes go mostly to the opposition parties that resemble it (E20). A formula specific to each country then turns votes into seats, and the same vote gives a very different assembly depending on the formula (E21).
In the game
The player leads the party at the head of the government. The “Politics” tab shows the country's institutions, who governs, and the table of parties with their family, their votes at the last election, their seats and today's polls, and clicking on a party shows its position on each of its sliders. The game is lost when the player's party no longer holds either the presidency or the head of the government (E22). In France, on 1 January 2026, Nouvel Élan leads a minority government with the Maison démocrate and Perspectives. The names of the parties and of their leaders are invented, but their positions, their votes and their seats are those of the data. When a game is created, the “Parties and coalitions” setting lets you switch the parties off, and an election then pits the government against all the others.
The basics
The game describes a party by what it stands for. In 2019, a survey, the Global Party Survey, asked experts in each country where each party stands on about twenty questions, such as the role of the state in the economy, immigration or respect for checks and balances. The game keeps twelve of them, which become twelve sliders, each going from 0 to 100, with 50 as the middle.
Two parties are close when their positions are similar across all the sliders. The game measures this closeness with a distance, the average gap between their positions, where large gaps count for more than small ones. It is 0 between two identical parties and 100 between two parties opposed on everything.
Each party also has a family, such as “liberal right” or “authoritarian nationalism”, which is the family whose centre is closest to the party's positions. It is used to present the party, but no calculation reads it. The studio wants it this way, because behaviour attached to the family would make two parties of the same family act in the same way, whereas positions on sliders leave each party in its own place.
The incumbent camp brings together the parties of the government, and the others form the opposition. In a coalition, one party leads the government and the others are its partners.
Finally, each country has its institutions, taken from databases on the world's political regimes. They say whether it votes, where its government comes from and how its votes become seats.
E19. Parties, their sliders and the institutions
In plain words
Each party is a list of twelve positions, from 0 to 100, which the game loads at the start of the game and never changes. A party therefore never moves, and no party is born or disappears during the game. At the start, each party has the votes and the seats of the last election that the sources describe, and each country has the government in office on 1 January 2026.
On the economy slider, where 0 means “more state” and 100 “more market”, Le Peuple indocile is at 10, Nouvel Élan at 66.9 and Héritage républicain at 80. On the populism slider, the Ralliement de la Nation is at 92.5 and the Maison démocrate at 22. Two parties can be neighbours on one slider and far apart on another. The Ralliement de la Nation is in the middle on the economy, at 55, but right at the top on restrictive immigration, at 96.9.
The twelve sliders:
| Slider | At 0 | At 100 |
|---|---|---|
| Economy: state or market | more state | more market |
| Spending or taxes | more public spending | lower taxes |
| Environment | for its protection | against its protection |
| Social values | liberal | conservative |
| Immigration | open | restrictive |
| Minority rights | defended | opposed |
| Women’s rights | defended | opposed |
| Stance on the world | multilateralism | nationalism |
| Populism | pluralist | populist |
| Liberal democracy | respected | undermined |
| Checks and balances | defended | rejected for a strongman |
| Public goods | for everyone | for its supporters |
Show the full formula and its sourcesWhere the positions, the votes, the seats, the governments and the institutions come from, and what these data leave out.
Each party is a profile: a position from 0 to 100 on each of the game's twelve sliders. Each slider is a question of the Global Party Survey 2019 (Norris 2020), put to experts in each country, on a scale from 0 to 10 brought to 0 to 100:
| Slider | Global Party Survey question | 0 | 100 |
|---|---|---|---|
economic_left_right | V4, economic left-right | the state in the economy | the market |
spending_taxes | V11, public spending or taxes | more public spending | lower taxes |
environment | V12, environmental protection | defends it | opposes it |
social_values | V6, social values | liberal | conservative |
immigration | V10, immigration | open policy | restrictive policy |
minority_rights | V15, rights of ethnic minorities | defends them | opposes them |
womens_rights | V14, women's rights | defends them | opposes them |
nationalism | V13, nationalism or multilateralism (reversed) | multilateralism | nationalism |
populism | V8, populist rhetoric | pluralist | populist |
illiberalism | V16, principles of liberal democracy | respects them | undermines them |
strongman | V21, checks and balances on the executive | defends them | rejects them |
clientelism | V17, who public goods go to | everyone | mostly its own |
A party also has a family, the name of the region of the sliders where it sits (“liberal right”, “authoritarian nationalism”). It is the family whose centre is closest to its profile, in weighted root mean square distance over the six sliders that name the families (the economy counts double, the environment half, populism, illiberalism and nationalism a quarter, the weights that best recover the ParlGov families). The family is only used for display, and no equation reads it. A party can claim a religion, or none. Each country has its institutions: a regime (democracy, electoral autocracy, closed autocracy), the type of its autocracy if it is one (party, personal, military, monarchy, oligarchy, theocracy), its head of state (president, constitutional monarch, ruling or absolute monarch, supreme leader), where its government comes from (parliament, the presidency, a ruling group) and the formula that turns votes into seats (E21). The game reads only three properties of these types: whether there are elections, and which ones (E23); where the government comes from (E22); which formula (E21).
At the start, each party has its share of the vote and of the seats at the last election the sources describe, brought to 100 over the parties that stand; the government is the one in office on 1 January 2026, with the party that leads it. In an autocracy without parties, the power (a royal house, a junta, a clergy) is a ruling group: a profile like a party, but one that stands in no election.
| Quantity | Value | Status | Source |
|---|---|---|---|
| the parties' positions | per party, twelve sliders | Global Party Survey 2019 (Norris 2020, CC0); for the parties it does not measure, ParlGov 2024 (CC0) on two axes, the other family sliders taken at the measured centre of the party's ParlGov family | |
| the families' centres | 14 families, six sliders | 8 families measured (the average of the GPS profiles of the parties that ParlGov puts in the same family), 6 placed by choice, each with its justification | |
| the starting votes and seats | per party | the most recent of: official results (ministries, electoral commissions), ParlGov, Database of Political Institutions 2023 (CC BY 4.0), Global Party Survey | |
| the starting government | per country | WhoGov 4.0 (Nyrup and Bramwell, CC BY 4.0), on 1 January 2026 | |
| the institutions | per country | Political Regimes of the World 3.0 (CC0), Database of Political Institutions 2023, and corrections sourced by hand |
Why. A “liberal” or “populist” government fixed once and for all would make two parties of the same family behave alike, and each new nuance would require one more rule. Positions on sliders, measured for 1,043 parties in 163 countries by a single survey, instead leave each party in its own place, and a slider is added with one line of data. The Global Party Survey is the only expert survey with this coverage whose licence allows a commercial game to use its figures (V-Dem and Wikipedia require share-alike, and the Chapel Hill Expert Survey shows no licence).
What it simplifies. The positions are those of 2019, fixed for the whole game. A party does not move, is not born and does not die. No open source measures the weight of religion in a party's politics, so there is no religious slider, only the religion a party claims. A party that no source places is left out, even when it matters (in France, the far right's allies gathered in the UDR group); so is a party under 1% of the vote, unless it governs. The starting votes do not date from the same year everywhere: the most recent official results where they have been collected, otherwise ParlGov (up to mid-2023), the DPI (the legislature of January 2023) or the GPS (up to 2019); when a source gives only the seats, the seats stand in for the votes. Liberal democracy and electoral democracy are not told apart, because the source that does so, V-Dem, is under a copyleft licence. The names of the parties and of their leaders are fictional.
E20. Each party's vote
In plain words
The incumbent camp wins or loses as many points as the score of E15 has won or lost since the last election. When it wins, each of its parties keeps its share of the camp, and the opposition pays in proportion to its votes. When it loses, its partners lose 2.2 times more than the party that leads it, in proportion to their votes, and these votes go to the opposition. An opposition party receives more of them the more votes it has and the closer it is to the government, since its appeal is halved every 35 points of distance. After a default, the far right of the opposition, that is, its parties that are both populist and conservative, gains up to a third of its own votes in five years, taken from the other opposition parties, and this gain then falls back to nothing after ten years. In a cohabitation, the president's party alone plays the role of the government, while the government's parties count as the opposition (E22).
In France, the government of Nouvel Élan, the Maison démocrate and Perspectives gathers a quarter of the 2024 vote. If the economy makes it lose 5 points, Nouvel Élan, which leads it, loses 13% of its votes, and its two partners lose 29% of theirs. The Ralliement de la Nation is the furthest from the government, at a distance of 41.9 points, but as it is also the largest party, it goes from 34.6% to 36.4%. The Alliance socialiste, much closer, goes from 11.7% to 12.7%.
In the formula:
| Symbol | What it is | In the example |
|---|---|---|
| \(G_0\) | the share of the government's parties at the last election | 24.6% |
| \(V_0\), \(V_t\) | the score of E15 on the day of the last election, and today | \(V_t - V_0 = -5\) |
| \(G_t\) | the government's share today | 19.6% |
| \(f\) | a floor, which the government's share never goes below | 1% |
| \(\Delta\) | the points the government loses | 5 |
| \(\ell_k\) | what party \(k\) of the government loses | |
| \(\omega_k\), \(H\) | the weight of the loss, 1 for the party that leads and \(H\) for a partner | \(H = 2.2\) |
| \(v_k\), \(v_k'\) | a party's share before and after | |
| \(d_k\) | the distance from party \(k\) to the government, over the twelve sliders | 41.9 for the Ralliement de la Nation |
| \(h\) | the distance that halves the appeal | 35 points |
| \(\gamma\), \(T\) | the far right's gain after a default, at its highest, and how long it lasts | 0.33; 10 years |
Show the full formula and its sourcesEvery parameter with its source, and what the equation leaves out.
Between two elections, and on polling day, the incumbent camp moves by as much as Abramowitz's equation has moved since the last election:
G0 is the share of the government's parties at the last election (or at the start), V0 what the equation of E15 gave on that day, Vt what it gives today, with the draw zE on polling day and without it between two votes. When the government gains, each of its parties keeps its share (vk × Gt/G0), and the gains are taken from the opposition in proportion to its shares. When it loses Δ = G0 − Gt points, its junior partners lose H times more than the party that leads it, relative to their share, and the opposition receives these votes all the more as it is close to the government:
dk is the distance from party k to the government: the square root of the mean of the squared gaps over all the sliders, between its profile and that of the government (the profiles of its parties, weighted by their seats). No party loses more than it has. What a partner can no longer lose falls on the other parties of the government, in the same proportions.
Under cohabitation (E22), the camp that the equation judges is the president's. Here the president's party alone plays the role of the government, with its share, its losses, and the distance of the other parties from its profile. The government's parties count as the opposition. V is then the equation of the coming election, without the time-for-change penalty when it is the assembly's (E15).
After a financial crisis, the far right rises. For T years after a default (E16), each far-right party in the opposition gains a share of its own vote that rises linearly up to γ halfway through, then falls back to nothing:
τ is the number of years since the default. This gain is taken from the other parties of the opposition, in proportion to their shares. The government does not pay for it, since it has already lost what the crisis costs it through E15. A party is far right if it is populist-conservative in the sense of the Global Party Survey's typology: populist beyond populist_threshold, and conservative, at least at crisis_extreme_social_values, on social values.
| Variable | Meaning | Unit | Bounds |
|---|---|---|---|
vote (v) | each party's share at the last election | % of the vote | 0 to 100, summing to 100 over the parties that stand |
vote_baseline (V0) | the vote of E15 on the day of the last election or of the last change of government, internal | % | not controlled |
| polls | each party's share if the vote were held today, for display | % of the vote | sum to 100 |
| Parameter | Value | Status | Source |
|---|---|---|---|
junior_loss_ratio H | 2.2 | Klüver and Spoon 2020, replication data (1,156 party-elections, 28 European countries, 1972-2017): junior partners keep 86.5% of their vote at the next election, the head of government's party 94.0%; losses of 13.5% and 6.0%, a ratio of 2.2 (medians 12.5% and 5.8%) | |
vote_proximity_half_distance h | 35 slider points | no study publishes a half-decay distance; the choice experiment of Gunderson and Marks 2026 (−0.100 in choice probability at one position apart out of five, −0.249 at two) gives 1.3 to 1.7 positions, that is 30 to 45 points out of 100: a fragile derivation, from a paper not peer-reviewed | |
government_vote_floor f | 1% | a numerical floor: no government in the data comes close to it | |
crisis_extreme_gain γ | 0.33 of their vote | Funke, Schularick and Trebesch 2016, table 5: the far-right vote grows by 8.4%, 16.4%, 21.0%, 27.5% and 32.8% (in relative terms) in years 1 to 5 after a financial crisis | |
crisis_extreme_years T | 10 years | same, p. 29-30: the peak around the fifth year, the effect down to 20% or less by the tenth, not significant after the eighth | |
crisis_extreme_social_values | 50 out of 100 | Global Party Survey 2019, codebook: its “Type_Populist_Values” typology counts a party among the conservatives when its position on V6 is 5 or more out of 10 (V6_Bin) | |
populist_threshold | 75 out of 100 | see E24 |
Why. Abramowitz's equation says how much the incumbent camp gains or loses. It does not say to whom. The junior partners of a coalition pay more than the party that leads it, which is the most robust result of Klüver and Spoon. Lost votes go first to neighbouring parties, as all spatial models of voting assume. After a financial crisis, the far right grows by a third in five years, in twenty advanced economies since 1870, and the far left does not move significantly.
What it simplifies. The incumbent camp moves as a block, following an equation estimated on US presidential elections, and its votes go to the opposition according to distance on the sliders alone. Neither the issues of the moment, nor the candidates, nor a party's own wear and tear count. Only a sovereign default counts as a financial crisis, since the model has no banking crisis. Funke et al. measure the far right in twenty advanced countries. The rule applies to all countries, and the far right is recognised there by two thresholds on sliders, whereas these authors draw up a list of parties. The half-distance of 35 points is a choice. The polls shown between two elections are those of the day, without the draw. They only follow popularity and growth.
E21. From votes to seats
In plain words
Under proportional representation, each party that reaches the country's threshold receives the same share of the seats as its share of the vote, measured against the parties that reach the threshold. Under a single-round majoritarian system, the largest party receives much more than its votes, because the game raises each party's votes to the power 2.5 before sharing out the seats. The mixed system gives a share of the seats by proportional representation and the rest by the majoritarian system. Under the two-round system, as in France, the game imagines every possible runoff, and each duel between two parties weighs more the more votes the two parties have. In each duel, the voters of the other parties vote for the closer of the two, and the seats of the duel are shared out to the power 2.5. For France, the studio prefers these duels to the single-round rule, which there would give three quarters of the seats to the largest party as soon as it passes a third of the vote.
In the 2024 elections, the Ralliement de la Nation won 34.6% of the vote, measured against the parties that stood. Under proportional representation with a threshold of 5%, it would have 35.6% of the seats, and under a single-round majoritarian system, 77.3%, a majority on its own. Under the two-round system, it has 37.8%. It wins each of its duels, but narrowly, because the voters of the other parties are closer to its opponent and tend to transfer to that opponent, and nearly half of the duels are played without it.
In the formula:
| Symbol | What it is | In the example |
|---|---|---|
| \(v_k\) | party \(k\)'s share of the vote | 34.6% |
| \(s_k\) | its share of the seats, depending on the formula | |
| \(\theta\) | the threshold to reach to get seats under proportional representation | 5% |
| \(x\) | the power of the majoritarian system | 2.5 |
| \(\lambda\) | the share of the seats by proportional representation, under the mixed system | |
| \(a_{kl}\) | the votes of party \(k\) in its duel against \(l\), transfers included | |
| \(d_{mk}\) | the distance between parties \(m\) and \(k\) | |
| \(h\) | the distance that halves a finalist's appeal | 35 points |
Show the full formula and its sourcesThe four formulas, the calendar of the French National Assembly, every parameter with its source, and what the equation leaves out.
On polling day, votes become seats through the country's formula:
Proportional representation gives seats in proportion to the votes of the parties that pass the country's threshold θ (if none passes it, they all share); the majoritarian system gives the power law, which gives the largest party more than its votes; the mixed system gives the country's share λ to proportional representation and the rest to the majoritarian system.
The two-round system plays the power law in each runoff duel. In a constituency, the two qualified parties are drawn in proportion to their votes, so the duel between k and l weighs a share of the seats proportional to vk·vl. In this duel, the voters of each other party m split between the two according to their proximity, halved every h points of distance, as in the runoff of a presidential election (E22):
dmk is the distance between the profiles of parties m and k (E19). With two parties, there is only one duel and nobody to transfer their vote, so it is the majoritarian formula. With more parties, a party that all the other electorates find distant wins fewer seats than votes, and a party of the centre wins more.
| Variable | Meaning | Unit | Bounds |
|---|---|---|---|
seats (s) | each party's share of the seats | % of the seats | 0 to 100, summing to 100 |
| Parameter | Value | Status | Source |
|---|---|---|---|
seat_exponent x | 2.5 | the cube law (exponent 3) is the theoretical value for a single-member system (Taagepera 1973); as measured, the exponent ranges from 2 to 2.6 in the United Kingdom and is about 2 in the US House (King and Browning 1987; Gelman and King 1994) |
| Quantity | Value | Status | Source |
|---|---|---|---|
| the formula, the threshold θ, the proportional share λ | per country | Database of Political Institutions 2023 (housesys, pr, thresh) and sourced corrections (λ for Japan, Mexico, Korea…; the two-round system of France) | |
| the rule of the two-round system | each duel weighted by the product of the votes, transfers by proximity, the power law within the duel | the cube law holds for a duel (Taagepera 1973); the transfers by proximity are those of the runoff of a presidential election (E22); that the two qualified parties of a constituency are drawn in proportion to their votes is a choice | |
| the calendar of the separately elected assembly | France: last election on 7 July 2024, five-year term | Constitution, article 12; electoral code, article LO 121 |
Why. What decides a parliamentary government is the seats, and the same vote gives very different seats depending on the formula. This is why a party at 35% governs alone in the United Kingdom, and never in the Netherlands.
When. The seats change at the election that decides who governs (E15), except where the assembly is elected separately, with its own calendar. They then change at its own elections, and the presidential election leaves them as they are. Only France has, for now, a separate calendar for its assembly. The other countries that elect a president keep the common rule, for lack of verified dates.
What it simplifies. There are no constituencies. The power law sums up at national level what hundreds of local duels do, with the same exponent everywhere, and a regional party that is strong in a few constituencies gains nothing more from it. Proportional representation is that of an infinite assembly: neither small constituencies nor the allocation method (d'Hondt, Sainte-Laguë) change the result. In the two-round system, there are no alliances and no withdrawals. Each party fields its candidate everywhere, the French left as four parties and not as one union, and the runoff pits only two candidates against each other (no three-way contest). A duel between two small parties weighs as little as the product of their votes, but it exists.