Decisions and votes

Each of the player's levers, that is, the fifteen budget lines (E26) and the policy rate, is held by a decision-maker: parliament, the government or the central bank. Only parliament votes. Who decides depends on the country's regime, through a general rule written in the game's data. A country can receive its own rules, which then take precedence over those of its regime. A decision that nothing names belongs to the government.

Tabling. A decision that parliament votes on is not taken on the spot. It is tabled as a bill, and voted on D days later. A decision that meets no vote (that of the government or of the central bank, that of a country where no party has a seat, or one that changes nothing in the value in force) applies on the 1^st of the following month, like any decision of the player.

The vote. On the set day, each party k that has seats votes, on that day's seats and against the value in force on that day. It first looks at how much of the lever it wants. This is its lean λ_k, its place on the lever's slider, from the neutral value towards the pole that a rise pushes towards, as a fraction of the half-scale.

x_k is the party's position on the lever's slider, n the neutral value of this slider and h its half-scale (50 out of 100); σ equals +1 when a rise in the lever pushes policy towards the upper pole of the slider, −1 towards the lower pole. When positive, the party wants the lever higher; when negative, lower. The second term is the lean that a lever can carry. The parties on one side of a second slider y favour raising it, whatever their place on the first one. w is its weight, and only the parties beyond the neutral value n_y, on the side the lean names, receive one. Today, only one lever carries one, pensions, which populist parties favour (see below).

This lean places the party's ideal level, around the level at which the country started the game:

v₀ is the value of the lever on the first day of the game; S is the gap between countries on this line, from the 10^th to the 90^th percentile of their starting values, over the countries whose budget the data measure (6.2 points of GDP for income tax, 2.3 for defence, 0.9 for security and justice); r is the reach (ballot_ideal_reach). A party at the end of its slider would move its country as far as the countries are apart from one another; a party in the centre wants the starting level.

The stake of a measure that takes the lever from the value in force v to the requested value v′, with Δ = v′ − v (Δτ, for a tax set by its rate, is the gap between the requested rate and the rate in force), is:

• Getting closer. The first term says how much the measure brings the lever closer to the party's ideal, times the intensity of its lean. As long as the measure does not go past the ideal, this term equals |λ_k| |Δ| in the direction the party wants, and −|λ_k| |Δ| in the other. Beyond the ideal, each point too many costs as much as a point gained.
• The cost of change. c (ballot_shock_cost) is the same for all parties. A large change worries even those who want its direction. It grows as the square of the size: 0.02 for one point, 2 for ten, 162 for ninety. For a tax set by its rate, it is counted on the rate gap Δτ, in points, at c_τ (ballot_rate_shock_cost): 0.01 for one point, 1 for ten, 4 for twenty. Counted on revenue, which levels off as the rate rises, an outsized rise would look small.
• The fear of the deficit. ΔB is what the measure does to the public balance, in points of GDP, +Δ for a revenue line and −Δ for a spending line. Only a widened deficit counts. A measure that reduces the deficit is judged on the rest. d (ballot_deficit_weight) is what one point of deficit costs a party at the centre of the slider of this fear, which is written in the game's data. It is the public spending slider, spending_taxes, on the side of lower spending. ρ_k is the party's place towards that side, from −1 to 1. The cost goes from nothing, for a party at the spending end, to double, for a party at the austerity end.

Then it votes:

On the day of the vote, each party's stake moves a little. The ballot above is read on the stake of the day:

s (ballot_swing) is the largest shift, in one direction or the other. Every value in the interval is as likely as any other, and each party has its own draw. The vote is therefore not drawn at random. A party whose stake is more than s away from each of its thresholds votes as the rule says, with certainty. Only a party whose stake is less than s away from a threshold hesitates, between the two ballots that this threshold separates. Its chance of voting for is

where ℓ is its threshold for voting for (−T for the party that leads, −t for a partner, o + i for the opposition), and likewise for voting against. The draw does not go through the game's generator. It is computed from the seed, the day of the vote, the country, the bill's rank among those the country votes on that day, and the party. The same game therefore votes the same way on every machine and at every replay, and nothing the player tables shifts the world's shocks.

Before the vote, the estimate states its margin. What the player reads when preparing a measure, and for each of their tabled bills, is the vote as each party weighs the measure today (ε = 0), followed by what the day of the vote can still shift:

• the parties that hesitate, those that have seats and more than one possible ballot;
• the range of seats for, and against, from the total of the parties certain of that ballot to the total of all those that may cast it;
• the chance of passing, the weight of all the ways in which the hesitating parties can vote that leave more seats for than against, each party drawing separately. It is counted exactly up to ten hesitating parties; beyond that, over 4,096 votes drawn from a fixed sequence, the same for every game, and so to within one point.

When nobody hesitates, the estimate is the vote, and there is neither a range nor a chance to state.

A partner's tolerance depends on its place in the government. Where the player puts together their government, the tolerance t of a partner is multiplied by what its party has received in posts and by what its ministers think of the player (E41). For a partner served in proportion to its seats, with neutral ministers, it is the one written here.

The party that leads the government votes for its measure as long as it does not cost it more than its tolerance T (ballot_head_tolerance). The measure is its own, so it puts up with more of it than a partner would. Beyond that it abstains, and at double it votes against. When the player holds the presidency under cohabitation (E22), the measure belongs to the president's party alone. That party votes for it within the same limits, and all the others, the government's included, vote on it as the opposition does. A coalition partner votes for it as long as it does not cost it more than its tolerance t (ballot_junior_tolerance). Beyond that it abstains, and at double it votes against. The opposition takes a bias o (ballot_opposition_bias) off its stake, because it votes against the government a little more often than its positions would suggest. Below the indifference threshold i (ballot_indifference), in either direction, a party abstains.

An example. France's income tax starts at 9.0 points of GDP, and the gap between countries there is 6.2 points. A left-wing party with a lean of 0.8 places its ideal at about 14 points. One more point is worth 0.8 to it, minus 0.02 for the change, so it votes for. Taken to 100, the tax ends up 86 points beyond its ideal, from which it was only 5 away. The stake is 0.8 × (5 − 86) = −64.8, and the change costs 0.02 × 91² ≈ 166 more. It votes against, like all the other parties, the government's included.

A tax by its rate. In France at the start, raising the top rate of income tax from 55.4 to 90% would raise only 1.1 points of GDP more, as the base responds. On today's base, it weighs 5.8 points more, and its 34.6 points of rate cost each party 0.01 × 34.6² ≈ 12. No party votes for it.

The slider of each lever is written in the game's data, with the pole towards which a rise pushes policy. A cut pushes towards the other one. A tax (E35) is voted on the slider of the line it belongs to, in points of GDP. v is what it raises today, and v′ what it would weigh at the requested rate on the base that the rate in force leaves (what it raises today, in proportion to the rate). v₀ and S are what it raised at the start and the gap between countries in what it raises. A rate rise thus stays a rise, even beyond the rate that raises the most, where revenue falls. ΔB, for its part, is what the line really gains once the base has responded. The cost of change is counted on the rate gap Δτ. A tax set by the level of its schedule, which has no rate to read, counts it in points of GDP, like a line.

For the three levers of E29, which change who pays for a line or who receives it (E29), v, v′ and the ideal are counted in points of output that they move from one quintile to others, starting from the distribution in the data, with the sign of the lever. The country starts from zero (v₀ = 0), and the gap S is the most that the lever can move in that country, at one of its ends. A party at the end of its slider would take the lever to that end. ΔB is what people's response does to the line: the revenue that the better-off no longer declare, the benefits that nobody claims.

The measure is passed when the seats for outnumber the seats against:

A tie rejects it. Once passed, it applies on the 1^st of the month after the vote. Once rejected, it leaves nothing but the news item of the vote, with its seats for and against and each party's ballot, as it was cast on that day. A bill that no longer meets a vote on the set day (nothing left to change, no parliament any more) passes.

The reform. Each measure is voted on alone, unless the player gathers several into a reform, which they name: budget lines (E26), each one once, tabled together and voted on as a block, on the same day. Everything passes, or nothing does. Each party adds up its stakes in the measures j of the reform, each one computed as for the measure alone, and votes on the sum as on a single measure:

e_k,j is the stake of party k in measure j alone (its position, the direction and the size of the measure). The ballot b_k follows the rules of a single measure, applied to c_k. The party that leads tolerates up to T, a junior partner up to t, and an opposition party takes off its bias o only once and abstains below the threshold i. The reform is passed like a single measure. A reform that meets no vote (that of a country whose government decides alone) applies in full on the 1^st of the following month. The policy rate, which is not voted on, does not go into a reform.

What the margin on the day of the vote does. On the first day, each lever put to the vote is moved by 0.5 and by 2 in its unit, downwards and upwards. A measure is certain when its chance of passing is 0 or 1; the others can turn against today's verdict.

France is the hard case. Its government holds 30% of the seats, and its bills pass because the opposition abstains. One measure in six is left to the day of the vote there, and five in six remain certain. Where the government has its majority, almost nothing moves. The size of s decides all of this:

(measures that can turn, out of the same totals; the row at 0.05 was measured before the migration laws, when France voted on 166 measures and not 198, and the measurement no longer reproduces it; the three parts of defence added twelve). At 0.05, seven measures out of ten were uncertain in France. Beyond the gap between the opposition's bias and its threshold (i − o = 0.05), a party that the measure leaves indifferent can already vote against. It is the first figure to tune.

Why. In a real country, the budget is voted on, and a government does not get it through without a majority, its own or another. So that the player sees what lies ahead, the vote takes time, and you know, party by party, who would vote for and against if the vote were held today. The rule that makes a party vote comes from spatial voting (Downs 1957; Enelow and Hinich 1984; Poole and Rosenthal 1985). People vote for what brings policy closer to their position, all the more clearly when it brings it much closer. The data do not say where each party places, in points of GDP, the level it wants. That level is constructed around the level at which the country starts, all the further away as the party is far from the centre, on the scale of what separates countries. The general rule does not block minority governments, which are numerous at the start: 77 governments out of 165 hold at most half of the seats, including those of France, Spain and Sweden.

What it simplifies. Each party votes as a block, with no rebellion by its members, and a lever is judged on a single slider. The unforeseeable part of the day of the vote is a single number, the same for all parties, all countries and all texts. It depends neither on the size of the party, nor on its discipline, nor on what happened between the tabling and the vote, and the parties' draws are independent of one another, with no wave that would carry off the whole opposition. A party that hesitates tips over as a whole, because its members do not split. The distribution is uniform over its interval, with no tail. Beyond s, there is no surprise, which no parliament guarantees. And the chance of passing stated before the vote is that of a vote held today. Between the tabling and the vote, the economy, the seats and the ministers' opinions still move, and the estimate moves with them. A party's ideal is constructed, not measured. It assumes that each party wants its country where it starts the game, moved according to its place on this single slider, and that the gap between countries gives the scale of what a party can want. The ideal no longer moves when the country changes. The cost of change is the same for all parties and all lines, and depends only on the size. The fear of the deficit looks only at what the measure does to the balance, not at the debt or at interest rates, so a heavily indebted country does not fear it more. The measure's effects on growth, unemployment or prices are not anticipated. The opposition's bias is the same for all its parties, with no bargaining and no negotiated support vote. There is no second reading, no shuttle between two chambers, no veto, no urgent procedure (the French 49.3) and no motion of censure tied to a bill. The motion of censure of E44 targets only the government. The delay is the same for all the measures of a regime. Non-player governments table nothing, because their budget follows their rule (E9, E24). The populist lean of pensions rests on a study of voters of the European radical right, but goes through the populism slider. It therefore also applies to the populist left, already favourable to pensions through its place on the left, and to populists outside Europe, whom the study does not cover. The other benefits, which the radical right wants to reserve for the “deserving”, keep the left-right slider alone. In a reform, a party does not bargain. It does not ask for the measure that bothers it to be withdrawn. It weighs the whole, and its stakes add up with no ceiling and no diminishing returns. No aggregation rule guarantees that a reform whose every measure would pass alone passes as a whole, nor the reverse. Parties that each reject a different measure can together form a majority against the whole. One point of rate costs the same for all taxes, whereas in France a point of VAT weighs twice as much GDP as a point of the top rate of income tax. The weight of a rate treats today's base as fixed, as if the parties did not expect it to respond. On a tax that few countries really levy (wealth, inheritance), the gap between countries is almost zero. Each party wants the starting level there, and the left votes against raising it.