Campaign
The two rounds of the presidential election, the debates and the promises, in the three months before an election that judges the player. This page covers equations E30, E31 and E32.
In plain words
Ninety days before an election that judges their camp, the player starts campaigning. In France, the presidential election is played in two rounds, fourteen days apart, and the two candidates who come first in the first round qualify for the runoff (E30). Seven days before the first round, a debate puts the player face to face with their main opponents, and seven days before the runoff, face to face with the other finalist, if their party is in the runoff. There they choose a line, defend their record, attack or promise, and each line wins them a few votes, with a share of chance (E31). During the campaign, they can also make up to three promises on budget lines, part of which voters grant them in advance, a larger part the more of their past promises they have kept. Once elected, they must keep them within two years, failing which each broken promise costs them popularity and credibility (E32).
In the game
The “Campaign” tab opens three months before the vote and shows the date of each round, the promises made and what each one promises to each group. The debate pauses the game, shows each opponent, what they stand for and what they propose, read in the unit in which the player sets each line, and waits for the player's line. Before choosing, the player sees what each line brings in on average and how far chance can move it from that. On election night, the news item gives the two candidates in the runoff and each one's share. The French presidential election has its runoff on 2 May 2027, so its first round on 18 April, and the campaign opens on 18 January. A player who has taken over the government facing an opposing president has no campaign, because the election judges the president's camp (E22).
The basics
In a two-round system, everyone first votes for their preferred candidate. If nobody wins more than half of the votes, the top two face each other two weeks later, and the voters of the eliminated candidates then move to whichever of the two is closest to them, or stay at home.
Studies of presidential campaigns find that debates move the polls very little, a point or two at most, while most of the vote is decided by the economy of the previous months (E15). The game therefore gives debates a small effect, with a share of chance that stands for the performance on the night.
Parties in power keep a good part of their election promises, more so when they govern alone than in a coalition. Voters still doubt them, so they grant in advance less than what is promised, and they put more faith in a candidate who has kept past promises. When a promise is broken, the disappointment is greater than the satisfaction a kept promise would have given, because a loss counts for more than a gain of the same size.
Show when a campaign opens and closesThe camp that the election judges, the election that comes first, and what the campaign leaves behind when it closes.
A campaign is open for the player when their party leads the camp that the next election judges (the government, or the president in cohabitation, E22), when the election is competitive (not controlled, E23), when the country has parties (E19), and when at most campaign_days days (90) remain before the next round. The next election is the one that comes first. It is either the one that decides who governs, through its first round where it has two, or that of a separately elected assembly (E21). A player whom the next election does not judge (they took the government facing a president from the other camp) has no campaign. Their promises and debates would judge the other camp.
The campaign closes on the day the election is decided. What it brought the player's camp (the gain from the debates, the anticipation of the promises) stops on that day. The promises of a player who has won become commitments.
| Variable | Meaning | Unit | Bounds |
|---|---|---|---|
| each country's campaign | the pending runoff, the debate, the gain from the debates, the promises, credibility, anticipation | — | state of the game, in its hash when it is not empty |
E30. The two rounds of the presidential election
In plain words
The first round takes place fourteen days before the runoff. On that day, the equation of E15 gives the score of the incumbent camp, with what the debates have brought it, and each party's votes follow from it (E20). A candidate who has more than half of the votes is elected, otherwise the top two go to the runoff. If the party in power is in it, the duel is again decided by E15, with the economic figures of the day of the runoff and the same draw as in the first round. If it has been eliminated, the two finalists share the votes of all the other parties, each one according to how close it is to them.
With the votes of the last election, the French first round qualifies Ralliement de la Nation and Nouvel Élan. Since Nouvel Élan leads the government and is in the runoff, it is E15 that decides the duel. If the government parties lose 5 points of the vote since the last election, Nouvel Élan is eliminated as early as the first round, and the runoff then pits Ralliement de la Nation against Le Peuple indocile. With a transfer that halves every 35 points of distance, Ralliement de la Nation wins with 59.2% of the votes.
The studio lets E15 decide the duel when the incumbent camp is in the runoff, because this is the equation that is calibrated on real elections, and because this way the outgoing camp loses about as often with two rounds as with one.
In the formula:
| Symbol | What it is | In the example |
|---|---|---|
| \(V_1\), \(V_2\) | the score of the incumbent camp, in the first round and in the runoff (E15) | |
| \(z^{E}_{t_1}\) | the draw on the day of the first round, used again in the runoff | |
| \(B\) | what the debates have brought the player's camp (E31) | |
| \(S_A\) | the share of finalist \(A\) in the runoff, when the incumbent camp is eliminated | 59.2% |
| \(v_k\) | the votes of party \(k\) in the first round | |
| \(d_{kA}\), \(h\) | the distance from party \(k\) to finalist \(A\), and the distance that halves the transfer | \(h = 35\) |
Show the full formula and its sourcesWhere and when the two rounds are held, the first round, the runoff with or without the incumbent camp, what it gives for France over fifty years, and what the equation leaves out.
Where. Wherever the data say that the president is elected in two rounds (today France alone, under its Constitution, article 7), that the election is competitive, and that a president governs (E19) or holds power separately from the assembly (E22). Everywhere else, the election is decided in one day, as E15 and E22 describe it.
When. The calendar dates an election by the day it is decided. For France, that day is the runoff (24 April 2022 and 2 May 2027). The first round takes place runoff_days days (14) earlier, and the runoff on the day in the calendar. The next term is counted from that day, whether the runoff takes place or not. The calendar does not drift.
The first round. On the day of the first round, the equation of E15 gives the incumbent camp
where B is what the debates have brought the player's camp (E31), and zero elsewhere. The votes of each party follow as in any election (E20). A candidate who has more than half of the vote is elected. Otherwise, the top two go to the runoff. The first-round news item gives their names, their votes and the day of the runoff. The votes of the first round are those of the election, and the following polls start from them (E20). The seats of the assembly, which is elected separately, do not change.
The runoff. If the party that leads the incumbent camp is one of the two, the duel is the vote of the two camps of E15, with the figures of the day of the runoff and the draw of the first round:
At 50 or more, it keeps power. If it was knocked out in the first round, the two others share the votes of all the parties that stand according to their proximity, halved every h points of distance (vote_proximity_half_distance, E20), as in the runoff of E22:
The larger share wins. What follows (who governs, the dissolution, cohabitation, the fate of the player) is the rule of E22, with the winner of the runoff in place of the one E22 computed on the same day. The news item on the election then gives, in addition to the score of the incumbent camp, the two candidates of the runoff, the one that the first round had put in the lead first, and the share of each, V2 and 100 − V2 in the first case, SA and SB in the second.
| Variable | Meaning | Unit | Bounds |
|---|---|---|---|
| the pending runoff | the day of the first round and of the runoff, the two candidates, the draw of the first round | — | state of the game, in its hash |
| V1, V2 | the incumbent camp's share of the vote of the two camps, in the first round and in the runoff | % | not controlled |
| SA | the share of candidate A in the runoff when the incumbent camp is not in it | % | 0 to 100 |
No new parameter. The equation is that of E15, and the transfer that of E22.
| Quantity | Value | Status | Source |
|---|---|---|---|
runoff_days | 14 days | Constitution, article 7: the second round takes place on the fourteenth day after the first | |
| the two-round countries | France | one source per country |
Why. With two dates, a campaign has a first-round evening, then two weeks in which the player knows their opponent and the transfers before debating. The runoff is still decided by E15 when the incumbent camp is in it, because E15 is what is calibrated. The outgoing camp loses about as often. Measured over France (fifty years, forty seeds, the game's shocks, no player), the share of presidential elections lost goes from 51.0% in one day to 55.2% in two rounds. The incumbent camp is knocked out in the first round in 15.8% of cases, wins the duel in 43.0% and loses it in 39.2%, and 2.0% are decided in the first round. The rest of the world, which votes in one day, does not change.
What it simplifies. There is a single draw for both rounds. The runoff adds only fourteen days of economy and the debate between the rounds. In a duel with the incumbent camp, the opponent does not count. E15 knows only two camps, and an incumbent facing the far right does no better there than facing the centre. Transfers are proximity alone, with no voting instructions, no withdrawals and no differential abstention between the rounds. A party fields one candidate, and its votes are those of its lists (E20). Only France votes in two rounds. Other countries elect their president this way (Brazil, Chile, Colombia, Peru…), sometimes with a threshold other than half (Argentina, Costa Rica), and they will come in with their source. Legislative elections are still computed in one day (E21).
E31. The debates
In plain words
Defending your record brings in what the record is worth, which popularity already sums up. At 50% popularity, the defence therefore brings in nothing on average, whereas it brings in 0.6 points at 60% and costs 0.6 at 40%. Attacking brings in half a point whatever the record, but with a risk twice as large as the other lines. Promising also brings in half a point, without this risk, and adds a promise from the catalogue. A random draw is added to each line, with a standard deviation of 0.75 points, and it stands for the performance on the night. What the debates bring in counts in the score of the player's camp until the day the election is decided. A first-round debate that has not been taken up closes with the first round, and the debate between the two rounds only takes place if the player's party is in the runoff.
With 58% popularity, defending your record brings in 3 × (2 × 58 − 100) / 100 = 0.48 points on average. Two nights out of three, the draw stays between −0.75 and +0.75 points, and the gain between −0.27 and 1.23 points. Attacking, barely better on average at 0.5 points, gives a gain between −1 and 2 points two nights out of three.
In the formula:
| Symbol | What it is | In the example |
|---|---|---|
| \(G\) | what the debate brings the player's camp, in points of the score of E15 | 0.48 on average |
| \(P\) | the day's popularity | 58% |
| \(a_D\) | what the defence is worth per unit of net approval | 3 |
| \(a_A\), \(r_A\) | the gain from attacking, and how many times its risk exceeds that of the other lines | 0.5; 2 |
| \(a_{Pr}\) | the gain from promising | 0.5 |
| \(\sigma_D\), \(z^{D}\) | the standard deviation of the draw, and the draw of the debate | 0.75 points |
Show the full formula and its sourcesWhen the debates take place, the opponents they show, every parameter with its source, and what the equation leaves out.
When. For the player in a campaign, debate_days days (7) before each round (before an election decided in one day, before each of the two rounds of a presidential election), or as soon as the campaign opens if it opens later. The debate pauses the game and shows the opponents. Before a first round, they are the debate_opponents parties (3) highest in the polls, the player's own aside. Before a runoff, it is the other finalist. The debate between the rounds is that of the duel. A player whose party is not in the runoff has none. The first-round debate closes with the first round, whether or not it was taken up, and what it brought stays acquired until the election. For each one, the debate shows what it stands for, that is, the two sliders on which it stands furthest from their neutral value, and on which side (E19). It also shows what it proposes, that is, the two budget lines whose ideal level (E25) is furthest from today's level, relative to the spread between countries, within the bounds of the lever. The player reads each proposal in the unit in which they set that line: its share of the budget for spending (E26), and for revenue the rate of its main tax that raises the desired amount, with the other taxes staying where they are (E35). This is the conversion that a concession to a protest movement already uses (E33). It changes neither the choice of the two lines nor the debate, and is only a way of reading them.
The lines. The player picks one, only once per debate:
P is the day's popularity, and zD a draw from a standard normal distribution, made on the day the debate opens (the country's election draw on that day, E15). The gain G is added to B, which counts in the vote of the two camps (E15, E30) in each round until the election is decided, and then goes back to zero. A debate left unanswered brings nothing.
What the player sees before choosing. For each line, what it brings at the average draw (zD = 0) and one standard deviation of what it brings (σD, or rA σD for the attack), in points of the vote. This is a reading of the equation above, not one more quantity, and the draw itself stays hidden until the answer.
| Variable | Meaning | Unit | Bounds |
|---|---|---|---|
| B | what the campaign's debates have brought the player's camp | points of the vote of the two camps | not controlled |
| the debate | the round it precedes and its day, its draw, the opponents, the line taken | — | state of the game, in its hash |
| Parameter | Value | Status | Source |
|---|---|---|---|
debate_defend aD | 3 points per unit of net approval | 0.6 points at 60% popularity, nothing at 50, −0.6 at 40; debates move polls little, a point or two at most (Holbrook 1996; Erikson and Wlezien 2012) | |
debate_attack aA | 0.5 points | a small gain, whatever the record: what defending a record at 58% brings | |
debate_attack_risk rA | 2 times the noise | attacking is the riskiest line | |
debate_promise aPr | 0.5 points | the gain of attacking without its risk; it is the commitment that costs (E32) | |
debate_noise σD | 0.75 points (standard deviation) | the effect of a debate rarely exceeds one or two points (Erikson and Wlezien 2012) |
| Quantity | Value | Status | Source |
|---|---|---|---|
debate_days | 7 days | a game design choice: the French debate between the rounds takes place a few days before the runoff | |
debate_opponents | 3 parties | a game design choice: what a debate screen can show legibly |
Why. A debate is a moment when the player acts on the vote other than through their policy of the previous months. It must weigh little, or it would crush everything else. Studies of presidential campaigns find that debates have weak effects. The gain from defending your record depends on the record. Popularity, which already sums it up (E12), decides it, and in the middle of a recession defending costs votes. Attacking brings in a little whatever the record, at the price of twice the risk.
What it simplifies. The opponents do not choose a line. Their performance is in the draw. What each one stands for and proposes is read from its sliders and from its ideals of E25. No programme is written, and a party at the end of a slider can propose a distant level. The gain is the same in every country and does not wear off, so two good debates are worth twice one. Only players debate. A non-player government has no debate, and its election does not depend on one.
E32. The promises
In plain words
A promise concerns a budget line, in one direction, by at least half a point of GDP, for example “cut VAT by half a point”. Since each group knows what this line brings it (E27), it computes what the promise would change in its income. Voters grant half of this in advance, multiplied by the player's credibility and by the weight that purchasing power has in popularity. If the player wins, the promise must be kept within 24 months. A kept promise raises credibility by 30% of the distance between it and 1, while a broken promise cuts it by half and costs, at a stroke, one and a half times the gain it had earned in advance.
A promise would bring 1.6% of income to low-income households. At the starting credibility, 0.6, they grant 0.5 × 0.6 × 0.5 × 1.6 = 0.24 points of popularity for it in advance. If the player wins the election and then keeps the promise, their credibility rises to 0.6 + 0.3 × (1 − 0.6) = 0.72. If they break it, credibility falls to 0.3, and low-income households take 1.5 × 0.24 = 0.36 points away from them at a stroke.
The studio has promises bear on budget lines rather than on results such as unemployment or growth, because those results would depend too much on chance.
In the formula:
| Symbol | What it is | In the example |
|---|---|---|
| \(\Delta y_{c,k}\) | what promise \(k\) would change in the income of cell \(c\), in % | 1.6 |
| \(A_{c,k}\) | what the voters of the cell grant in advance, in points of popularity | 0.24 |
| \(\alpha\) | the share of the promised gain granted in advance, before credibility | 0.5 |
| \(\kappa\) | the credibility of the player's promises | 0.6 |
| \(a_y\) | the weight of purchasing power in popularity (E12) | 0.5 |
| \(g\), \(l\) | what credibility gains when a promise is kept, and what it loses when one is broken | 0.3; 0.5 |
| \(b\) | what a broken promise costs, as a multiple of the gain granted in advance | 1.5 |
Show the full formula and its sourcesThe catalogue of promises, what voters expect from them, the commitment after the election, every parameter with its source, what it gives for France, and what the equation leaves out.
Making a promise. During their campaign, the player picks at most promise_slots promises (3) from the catalogue, or makes one in a debate (E31). A promise bears on a budget line, in one direction, by at least a given size, in points of GDP, for instance “cut VAT by half a point of GDP”. Its target is the level of the line on the day it is made, plus or minus the size, within the bounds of the lever. A line carries only one promise at a time.
What voters expect from it. Each cell of the population knows what a budget line brings it or costs it (E27). A promise k that has been made and not yet kept changes its income by
at today's output and unemployment. Voters grant a share of it in advance, at the weight purchasing power has in popularity (E12), according to the player's credibility κk on the day of the promise:
The country's popularity target (E12, E28) gains the average of the Ac,k over its voters, and that of each group gains the average over its own (the weights of E28), with all the promises of the campaign added up. These gains are recomputed on the 1st of each month and on the day of a promise, and stop on the day the election is decided. A promise kept before the vote has nothing left to wait for. What the line brings then goes through E27 and E28 like any decision.
After the election. If the player's camp has won (it keeps the presidency or the government at the election that decides who governs, or the majority at the assembly election, E22), each promise becomes a commitment, due months months after the day of the decision (24 months in the catalogue). It is kept on the day the line in force reaches its target, and broken on the due date if the line has not reached it. Parliament votes on the budget lines (E25), so a promise can run into a majority that refuses it. If the player's camp has lost, or if the player loses power, their promises no longer bind them.
Kept, broken. The player's credibility, the same for all their promises and from one campaign to the next, starts from κ0:
A broken promise costs each group, and the country, at once b times what the missing gain would have been worth to it in advance, with losses counting for nothing. The missing gain runs from the level of the line on that day to the target:
Popularity then climbs back towards its target at the pace of E12.
| Variable | Meaning | Unit | Bounds |
|---|---|---|---|
| κ | the credibility of the player's promises | — | 0 to 1 |
| A | what voters grant the campaign's promises, country and groups | points of popularity | not controlled |
| the promises | for each one: line, direction, target, day, credibility on that day, due date, state | — | state of the game, in its hash |
| Parameter | Value | Status | Source |
|---|---|---|---|
promise_anticipation α | 0.5 | the share of the promised gain granted in advance, before credibility; no study measures it in this form | |
promise_credibility_start κ0 | 0.6 | parties in power keep a good share of their promises, more when alone than in a coalition (Thomson et al. 2017), and voters believe they do so less than they actually do | |
promise_credibility_gain g | 0.3 of the way to 1 | a promise kept: from 0.6 to 0.72 | |
promise_credibility_loss l | 0.5 of credibility | a promise broken: from 0.6 to 0.3; breaking costs more than keeping brings | |
promise_betrayal b | 1.5 times the gain granted in advance | a loss weighs more than a gain of the same size: Tversky and Kahneman (1992) estimate the ratio at 2.25; 1.5 is below that |
| Quantity | Value | Status | Source |
|---|---|---|---|
campaign_days | 90 days | a game design choice | |
promise_slots | 3 promises | a game design choice | |
| the catalogue | seven promises, on the lines that go through household incomes (E27): cut VAT, income tax, contributions, corporate tax; raise property tax, pensions, other benefits | the game's data |
The results. Measured on France on 18 January 2027, the day the campaign opens (seed 1, no shocks), and at the starting credibility, cutting VAT by half a point of GDP promises 1.6% of income to low-income households, 5.7% to the unemployed and 1.0% to retirees, and is worth 0.23 points of popularity to the country in advance. Raising the other benefits by half a point promises 8.1% to the unemployed and is worth 0.27 points. Cutting income tax promises 1.3% to well-off households and 0.3% to low-income ones, and is worth 0.10 points. Raising property tax costs 0.13. Three promises are thus worth a few tenths of a point of popularity, that is, a tenth of a point of the vote of the two camps (E15). This is the order of magnitude of what the model grants the same measure once taken (E12), reduced in advance by α and κ.
Why. The population in groups makes this possible. Each group knows what a line brings it. A VAT cut pleases every quintile, and an income tax cut pleases the last one. The dilemma comes from E25. Parliament can refuse the promised measure, and a coalition keeps its promises less than a single party does (Thomson et al. 2017).
What it simplifies. Promises bear only on lines, not on results (unemployment, growth), which would depend too much on chance. Voters anticipate only the direct effect on their income, not what the measure will do to the economy or to the deficit. The lines that do not go through household incomes (health, education, defence, security, administration) promise nothing to anyone in E27, so they are not in the catalogue. A promise is kept as soon as the line reaches the target, even if it moves away from it afterwards. The other parties promise nothing. Breaking a promise is a shock that fades at the pace of popularity, not a grudge that lasts until the next election. Credibility does not depend on the coalition.
- Erikson, R. S. and Wlezien, C. (2012). The Timeline of Presidential Elections: How Campaigns Do (and Do Not) Matter. University of Chicago Press.
- Holbrook, T. M. (1996). Do Campaigns Matter? Sage Publications.
- Thomson, R., Royed, T., Naurin, E., Artés, J., Costello, R., Ennser-Jedenastik, L., Ferguson, M., Kostadinova, P., Moury, C., Pétry, F. and Praprotnik, K. (2017). “The Fulfillment of Parties' Election Pledges: A Comparative Study on the Impact of Power Sharing”. American Journal of Political Science, 61(3), p. 527-542.
- Tversky, A. and Kahneman, D. (1992). “Advances in Prospect Theory: Cumulative Representation of Uncertainty”. Journal of Risk and Uncertainty, 5(4), p. 297-323.
- Constitution of 4 October 1958, article 7.