Protest movements

The grievance. On the first of each month, the groups read their incomes (E27). The change in the income of a person in group g since the government took office splits in two. One part is what the state's decisions have changed in it, p_g, that is, the person's income today against the income they would have with the budget lines the government found. The other part is what the market has changed in it, m_g, that is, output and unemployment, with the lines of that time. The loss the group feels, in %, weighs the two as the group weighs them in its vote (E28):

with b_P = own_income_policy and b_M = own_income_market. A loss due to a decision of the state counts four times as much as a loss due to the economic situation.

Habituation. A group gets used to the loss it lives with. Each day, what it has got used to, H_g, closes part of its gap with the loss in force (the one read on the first of the month, not a measure that has only been announced, which nobody bears yet), and what it still feels is the remainder:

with the half-life h_H = unrest_habituation_half_life_days. A loss that persists is felt half as much every h_H days. A gain is not a loss to get used to. H does not go below zero, and losing that gain later is felt in full. Once the loss is given back, H falls back at the same pace. A new government starts again from H = 0, as it starts again from a zero loss (E28).

Anger. The anger that the felt loss calls for, from 0 to 100:

where L̄ = unrest_grievance is the loss from which a group protests, and κ = unrest_anger_per_point the points of anger per point of loss beyond it.

The start. On the same day, each group that is not already in the streets, and whose last movement ended at least unrest_cooldown_days days ago, takes to the streets if the anger its loss calls for reaches at least the end threshold (unrest_end_anger). A movement that would end on the same day is not a movement. Its anger starts from zero. Several groups can be in the streets at once, each in its own movement, with its anger, its demand and the responses it has received. A group leads only one at a time. Groups that start on the same day are ordered as in the data. The anger called for by a movement under way is read again each month, and each day in the player's country (see the announced measures).

Each day, anger A closes part of its gap with what the loss calls for:

with the half-life h_A = unrest_anger_half_life_days. Beyond unrest_riot_anger, the protests turn into riots. Once anger is back below it, the riots calm down into protests. When anger and what the loss calls for are both below unrest_end_anger, the movement dies out. A movement that nobody responds to therefore subsides on its own. The riots calm down, then the movement dies out, as the group gets used to its loss, with the measure that started it still in force.

The demand. Each group asks for a budget line, raised or cut. Retirees ask for their pensions, low-income households and the unemployed for the other benefits, the middle class for less income tax, well-off households for lower property taxes, young people for education, and rural dwellers for lower excise duties (fuel). A group asks for the line where the government found it, if the government has moved it, or announced a move, against the group. Otherwise it asks for unrest_demand_step points of GDP more in its direction, starting from the announced value if there is one. The demand is fixed when the movement starts, within the bounds of the lever.

Riots cost output the first time a movement turns to them. They act on the same day like a world event that would change output in the first year by unrest_riot_output (E18), that is, a jump in the output gap that fades at its own speed. Relapses of the same movement cost nothing more. Studies measure the episode, not each night of clashes. Two groups that turn to rioting each cost their share.

The announced measures

A measure of the player does not apply on the day they take it. Once decided, it waits for the first of the following month. Once put to a vote, it waits for the assembly's vote (E25). In between, it is announced. As long as their government has announced a measure that moves a budget line (the amount or share of a spending line, E26; the rate of a tax, E35; the split of a line, E29) and that is not yet in force, the groups of the player's country read their loss L_g each day as if the announced lines already applied. These lines are computed as the first of the month will compute them, with the rest of the economy as it is on that day. The start of a movement is judged each day on this reading. People therefore take to the streets against a measure on the day it is announced, without waiting for it to apply or to be voted on.

A measure that is withdrawn, or rejected by the assembly, stops calling for anger on the same day. The loss becomes that of the first of the month again, and the movement it had launched subsides and then dies out. Once passed, it waits for the first of the following month, still announced, then applies, and the month's reading finds it in force. When several measures are announced on the same line, the last one counts.

Non-player governments announce nothing. Their fiscal rule decides on the same day, and their groups read their incomes on the first of the month.

The government's responses

The player responds to each movement in their country whenever they wish, between two days, by naming the group. A response affects only that group's movement. Each response is an action in the player's log, replayed when a save is loaded. Conceding to one group can make up for the loss of another. Withdrawing a pension cut also calms the low-income households it was making poorer.

• Conceding first withdraws what the government had announced on the demanded line and that is not yet in force. This means any measure that moves it (its amount, its share, the rate of a tax that raises it, its split), whether the decision waiting for the first of the month or the measure in the bill. A bill left with no measure is withdrawn, and a reform keeps its other measures. If the line in force is not already what the movement demands, conceding then orders the demand as an order of the player. A spending line is ordered by its amount. A revenue line, which the player sets only through its taxes (E35), is ordered by the rate of its main tax (the first of the taxes that raise it: income tax, VAT, excise duties, property tax…), the rate that brings the line back to the amount demanded with the other taxes unchanged. That rate is found by halving 64 times the interval between the rate in force and the bound on the requested side. If decided, the measure applies on the first of the following month. If put to a vote, it waits for the assembly's vote (E25), which can reject it. The loss then comes back, and anger with it. Anger at once loses the share unrest_concession_calm. Once the measure is withdrawn, or the demand announced, the loss the group reads is made up, the anger it calls for falls back, and the movement dies out. Once per movement. It is refused when the line is already what the movement demands and nothing is announced against it.
• Receiving them (negotiating) removes unrest_talks_calm points of anger. Once per movement.
• A firm hand removes unrest_force_calm points of anger and costs unrest_force_popularity points of popularity, in the country and in the group, which then return towards their target at the pace of popularity (E12). Since the loss remains, anger climbs back towards what it still calls for, and the riots come back as long as the group has not got used to the loss enough.
• Letting it run changes nothing. The movement subsides as the group gets used to its loss.

Non-player governments use a firm hand each time a riot breaks out. Their movements last as long as the group feels its loss. They last until it gets used to the loss, until the economic situation makes it up, until their fiscal rule gives back what it had taken, or until a new government arrives. Its groups then judge it from the economy it finds (E28), and the loss starts again from zero.

The news items report each turning point of a movement in the player's country. Elsewhere, they report its start, its first riot, the firm hand that answers it and its end.

The results

Measured:

• A cut played by hand. France, with its government deciding its budget alone, cuts its pensions by two points of GDP on the first day (without the parties, because the National Assembly rejects the cut with 60% of the seats). The cut applies on 1 February. On that day, the state has taken 15.4% of their income from retirees, 6.1% from low-income households, 2.8% from the middle class and rural dwellers, 1.1% from well-off households, and nothing from young people or the unemployed. The market has taken 0.7% from them, and 0.6% from the unemployed. Retirees and low-income households take to the streets on the day of the announcement, 1 January (day 0), each in its own movement. On 2 February, the retirees' anger stands at 67 out of 100, that of low-income households at 28, and that of the middle class and rural dwellers, who lose barely more than the threshold, at 6. The other groups stay at home. The retirees' protests turn into riots on 27 January (day 26). Over the year that follows the cut, output loses 0.20% compared with the same game without the movements, and it is the riots themselves that cost it. The same game in which a riot costs nothing (unrest_riot_output at zero) gives back the whole gap. A country in the streets does not receive the same events, however (E55). In this game, these are mayors asking for a curfew and clashes on the fringes of a march, on top of the bridge that threatens to collapse in both games. The measurement leaves them unanswered, and they weigh nothing on output that year. When the government concedes at the first riot (day 27), before the cut applies, the cut is withdrawn and the movement dies out 53 days later. When it concedes once the cut is in force (day 32), pensions are given back on 1 March and the movement dies out 55 days later.
• The same cut, never answered, without an election, so that the same government stays. The retirees' anger stands at 96 after three months, 76 after six and 27 after a year. The riots calm down on day 235, and the movement dies out on day 527, with the cut still in force. With a half-life of one year instead of six months, anger stands at 96, 99 and 66, then 24 after two years. The riots calm down on day 410, and the movement dies out on day 905. Without habituation, anger rises to 100 and stays there, and the riots never end.
• The same cut, tabled in the National Assembly, with the parties. Retirees take to the streets on the day of tabling (day 0), the National Assembly rejects the cut on 31 January (day 30), and the movement, which nothing calls for any more, dies out on 14 April (day 103).
• The world without a player, over ten games of twenty years. There are 16.0 movements per country per century in advanced countries, 7.6 in emerging ones and 0.3 in low-income countries. Of these movements, 5%, 6% and none turn into riots, and 18%, 30% and none start when another group in the country is already in the streets. A movement lasts 108, 77 and 193 days at the median. There are up to seven at once in a single country. What the state had taken (p_g) would have been enough on its own, before any habituation, to pass the loss that puts a group in the streets (2.5%) in 61% of the starts in advanced countries and 73% of those in emerging ones. What the market had taken, weighed as the group weighs it, would have been enough in 40% and 27%. The countries that see the most are Venezuela, Nauru, Tuvalu, Macao, Timor-Leste, Brunei, Libya, the Northern Mariana Islands, Saint Martin and Saint Kitts and Nevis. Five of these ten (Nauru, Tuvalu, the Northern Marianas, Saint Martin, Saint Kitts and Nevis) are small territories whose groups are estimated from a neighbour. Saint Martin, which its routes empty (E85), came onto the list with them. France sees 9 in two hundred years of games, the United States 19, Germany 9, Greece 43 and Argentina 48.
• Where they come from, in the same ten games.
• A few countries make the average. Advanced countries see 16.0 per country per century on average, but 8.0 at the median. Nine in ten have fewer than 51.0, the hardest hit has 106.0, seven have none, and the ten that have the most make up 42% of the total. In emerging countries, the median is 0.5 for an average of 7.6. Of 110 countries, 45 have none, and ten make up 72%. Three of the ten leading countries (Venezuela, Macao, Timor-Leste) are among those that the model itself holds out of its domain (a hyperinflation, a sovereign wealth fund that it does not know).
• What was moving on the day of the start. In 4% of the starts in advanced countries and 34% of those in emerging ones, the country was shut out of the markets after a default, which closes its primary deficit at a stroke (E16). Otherwise, what the state had taken was enough on its own in 58% and 46% of starts, although primary spending had fallen by more than 2% in a year in only 16% and 22% of starts. For the rest, either the fall was slower, or it does not go through total spending, and the measurement does not tell them apart. Otherwise again, what the market had taken was enough on its own in 28% and 12%. Two groups account for four starts in five, all countries together: the unemployed (42%) and retirees (40%).
• The same games, with one setting changed, and no other equation. Non-player budgets held still (fiscal_half_life_days infinite): 12.4 per advanced country per century instead of 16.0. What the state had taken is now enough on its own in only 15% of starts instead of 54%, but a country that no longer adjusts its budget defaults, and it is shut out of the markets in 56% of starts instead of 14%. Non-player governments with their rules alone (without E24): 14.7 on average, and the median goes from 8.0 to 5.5. The grievance raised by one point (a loss of 3.5% instead of 2.5%): 7.1 on average, 1.5 at the median; by two and a half points (5%): 2.8, and a median of zero. The control run (budgets held still, rules alone, no default), where a non-player government no longer decides anything: 1,300 movements remain, 5.3 per advanced country per century, none of them where what the state had taken was enough on its own; what the market had taken is enough on its own in 1,298 of them. Nothing else in the model is therefore read as a decision of the state.
• Almost none in low-income countries: 14 in all, of which more than three quarters (79%) start when the country is shut out of the markets after a default, 21% because of what the state has taken, and none because of what the market has taken.

What it simplifies

Everything is a choice, except the weight of the market, taken from E28. No study gives, in points of anger, the loss of income that leads people into the streets, nor the cost of a riot for a given country. A movement follows a single group. Several groups in the streets make several movements, with no common front and no shared demand, and a group that loses barely more than the threshold leads a movement as well as a ruined group does. It takes no more anger to start than to last. Habituation is the same for everyone. A retiree gets used to a reduced pension at the pace at which a well-off household gets used to a tax, and to a loss of 15% as to a loss of 3%; its half-life is a choice that nothing measures. It applies only to the streets. The group's opinion (E28) does not get used to the loss, and a group that has gone back home still judges its government on what it has taken from it since it arrived. Habituation runs on the loss in force, not on an announced measure, and on the loss read on the first of the month. Anger feeds only on the loss of income. Neither inflation as such, nor youth unemployment, nor unpopularity, nor contagion from one country to another, nor social networks, nor past repression gives rise to it. The loss is measured from the government's arrival, so a new government wipes out the grievances against the old one. Nothing depends on the regime. In a democracy and in a dictatorship, groups take to the streets at the same thresholds, and a firm hand costs the same popularity there. Riots cost only output, with no deaths, no damage and no risk premium on the debt. Conceding goes through the usual vote, and a parliament can refuse what the street would obtain. Non-player governments never concede and never negotiate. The demand is a single line, fixed when the movement starts, in points of GDP. A group claims what a revenue line takes from it, not a rate, and conceding on a revenue line touches only its main tax, never the other taxes that raise it. An announced measure is judged as if it already applied in full. Neither the chance that it is rejected nor the time it will take to come tempers anger.

Sources

• Ponticelli, J. and Voth, H.-J. (2020), “Austerity and anarchy: Budget cuts and social unrest in Europe, 1919-2008”, Journal of Comparative Economics 48 (1).
• Hadzi-Vaskov, M., Pienknagura, S. and Ricci, L. A. (2021), “The Macroeconomic Impact of Social Unrest”, IMF Working Paper 21/135.
• Healy, A., Persson, M. and Snowberg, E. (2017), for the weight of the state and the market: see E28.