Quadratic Voting with Asymmetric Information about Policy Effects

I recruit participants on Amazon Mechanical Turk and Turker Nation. There are two treatments: the corruption game and the pollution game. Participation will occur in two stages. First, participants will learn the game and participants who succeed in learning the game will be awarded a qualification that indicates their mastery. Each session will start with instructions. Next, participants will answer a comprehension quiz on the mechanism. Each participant can attempt the quiz an unlimited number of times. Participants will be paid $1 if they successfully complete the comprehension quiz. If a participant decides that the comprehension quiz is too difficult, that participant may give up and will be awarded 50 cents as compensation for time spent reading instructions and trying the quiz. For the interactive treatments, I will send out a when2meet link. If I can find groups of three participants who can play at the same time, have learned the game, and consent to participating in research, I will recruit them for an interactive treatment. There will be 20 periods where subjects use both Quadratic Voting (QV) and majority voting and receive the sum of the payoffs from both mechanisms and 20 periods of the groups’ choice of mechanism. Each group will consist of three participants. Each participant will receive 24 points during each of the first 20 rounds and 16 points during each of the last 20 rounds. In all rounds, ties will be broken randomly.
One treatment is the corruption game. In each round, one participant will be chosen uniformly at random to be an official and the other two participants will be taxpayers. In each period, it is common knowledge that an official has a 50% chance of being corrupt. The official knows whether he is corrupt, but the taxpayers do not. Each round, participants decide whether to audit the government. If the government is audited, each participant loses 2 points. If the government is not audited and the official is corrupt, the official gains 6 points and each taxpayer loses 8 points. For majority voting, each participant will vote for or against auditing the government and the government will be audited if and only if a majority votes to audit. For the QV rounds, each participant can spend up to 8 points purchasing votes for or against auditing the government. Participants must spend a whole number of points purchasing votes. The number of votes purchased is equal to the square root of the number of points spent and the option with the most votes will win. Each participant’s voting expenditure will be evenly divided among the other participants.
The other treatment is the pollution game. In each round, one participant will be chosen uniformly at random to be a factory owner and the other two participants will be taxpayers. The group considers requiring the factory owner to modify his or her polluting factories to prevent them from generating pollution. In each period, it is common knowledge that there is a 50% chance that modifying each factory costs the owner 2 points and a 50% change that modifying each factory costs the owner 8 points. The owner knows the cost of modifying a factory but the residents do not. During each of the first 20 rounds, the factory owner has 2 factories. In each of those rounds. participants decide whether to require the owner to modify those factories. The group decides whether to require the owner to modify the first factory using majority voting. Each participant votes for or against requiring a modification and the option with the most votes wins. The group decides whether to require the owner to modify the second factory using Quadratic Voting. For the QV rounds, each participant can spend up to 8 points purchasing votes for or against requiring the modification of the second factory. Participants must spend a whole number of points purchasing votes. Each participant’s voting expenditure will be evenly distributed among other participants.
Participants will use majority voting to decide whether to use majority voting or QV for the final 20 rounds. Participants will all be playing at the same time and will learn the results of each group decision before making the next one. Participants will receive a $2 show-up fee. I send participants to a waiting room after they read the instructions. I attempt to match groups of three participants in the waiting room. In order to receive payment, I require participants to remain in the waiting room for 5 minutes. A timer displays the initial time remaining until participants can leave the waiting room and receive payment. Once the timer hits zero, participants may either leave and collect a payment of $2 or increase the timer to 2 minutes in order to continue searching for a group. Participants have 2 minutes to make each set of decisions and participants who fail to make decisions in time are removed from the experiment and paid for the sections they have completed. After each decision that is not the last decision, participants have 30 seconds to review the results of the previous decision. If some members of a group disconnect, the remaining members of the group are allowed to finish the experiment. Instead of the normal rewards, participants in a group that has fewer than 3 members remaining receive 24 points per round. Participants will be paid 2 cents per point accumulated.

2020-09-13

2020-11-13

The difference in welfare between Quadratic Voting and majority voting and the fraction of groups who chose Quadratic Voting.

I will calculate the difference in welfare using the first 20 rounds.

I recruit participants on Amazon Mechanical Turk and Turker Nation. There are two treatments: the corruption game and the pollution game. Participation will occur in two stages. First, participants will learn the game and participants who succeed in learning the game will be awarded a qualification that indicates their mastery. Each session will start with instructions. Next, participants will answer a comprehension quiz on the mechanism. Each participant can attempt the quiz an unlimited number of times. Participants will be paid $1 if they successfully complete the comprehension quiz. If a participant decides that the comprehension quiz is too difficult, that participant may give up and will be awarded 50 cents as compensation for time spent reading instructions and trying the quiz. For the interactive treatments, I will send out a when2meet link. If I can find groups of three participants who can play at the same time, have learned the game, and consent to participating in research, I will recruit them for an interactive treatment. There will be 20 periods where subjects use both Quadratic Voting (QV) and majority voting and receive the sum of the payoffs from both mechanisms and 20 periods of the groups’ choice of mechanism. Each group will consist of three participants. Each participant will receive 24 points during each of the first 20 rounds and 16 points during each of the last 20 rounds. In all rounds, ties will be broken randomly.
One treatment is the corruption game. In each round, one participant will be chosen uniformly at random to be an official and the other two participants will be taxpayers. In each period, it is common knowledge that an official has a 50% chance of being corrupt. The official knows whether he is corrupt, but the taxpayers do not. Each round, participants decide whether to audit the government. If the government is audited, each participant loses 2 points. If the government is not audited and the official is corrupt, the official gains 6 points and each taxpayer loses 8 points. For majority voting, each participant will vote for or against auditing the government and the government will be audited if and only if a majority votes to audit. For the QV rounds, each participant can spend up to 8 points purchasing votes for or against auditing the government. Participants must spend a whole number of points purchasing votes. The number of votes purchased is equal to the square root of the number of points spent and the option with the most votes will win. Each participant’s voting expenditure will be evenly divided among the other participants.
The other treatment is the pollution game. In each round, one participant will be chosen uniformly at random to be a factory owner and the other two participants will be taxpayers. The group considers requiring the factory owner to modify his or her polluting factories to prevent them from generating pollution. In each period, it is common knowledge that there is a 50% chance that modifying each factory costs the owner 2 points and a 50% change that modifying each factory costs the owner 8 points. The owner knows the cost of modifying a factory but the residents do not. During each of the first 20 rounds, the factory owner has 2 factories. In each of those rounds. participants decide whether to require the owner to modify those factories. The group decides whether to require the owner to modify the first factory using majority voting. Each participant votes for or against requiring a modification and the option with the most votes wins. The group decides whether to require the owner to modify the second factory using Quadratic Voting. For the QV rounds, each participant can spend up to 8 points purchasing votes for or against requiring the modification of the second factory. Participants must spend a whole number of points purchasing votes. Each participant’s voting expenditure will be evenly distributed among other participants.
Participants will use majority voting to decide whether to use majority voting or QV for the final 20 rounds. Participants will all be playing at the same time and will learn the results of each group decision before making the next one. Participants will receive a $2 show-up fee. I send participants to a waiting room after they read the instructions. I attempt to match groups of three participants in the waiting room. In order to receive payment, I require participants to remain in the waiting room for 5 minutes. A timer displays the initial time remaining until participants can leave the waiting room and receive payment. Once the timer hits zero, participants may either leave and collect a payment of $2 or increase the timer to 2 minutes in order to continue searching for a group. Participants have 2 minutes to make each set of decisions and participants who fail to make decisions in time are removed from the experiment and paid for the sections they have completed. After each decision that is not the last decision, participants have 30 seconds to review the results of the previous decision. If some members of a group disconnect, the remaining members of the group are allowed to finish the experiment. Instead of the normal rewards, participants in a group that has fewer than 3 members remaining receive 24 points per round. Participants will be paid 2 cents per point accumulated.

Online random number generator

Randomization is done each round on the group level.

No

28 groups of 3 individuals

28 groups

14 group playing the corruption game and 14 groups playing the pollution game

Analysis_Plan.pdf

Quadratic Voting (QV) is a promising technique for improving group decision-making by accounting for preference intensities. QV is a social choice mechanism in which voters buy votes for or against a proposal at a quadratic cost and the outcome with the most votes wins. In some cases, individuals are asymmetrically informed about the effects of legislation and therefore their valuations of legislation. For instance, anti-corruption legislation is the most beneficial to taxpayers and the most detrimental to corrupt officials when corruption opportunities are plentiful, but government officials have better information than taxpayers about how many corruption opportunities exist. I provide an example of a setting in a large population where QV does not achieve approximate efficiency despite majority voting achieving full efficiency. In this example, a society considers an anti-corruption policy that protects taxpayers from corruption by deterring corruption. Officials know whether corruption opportunities exist, but taxpayers are uncertain about whether corruption opportunities exist. I present surprising experimental results showing that in one case where theory predicts QV will perform poorly and majority voting will perform relatively well, QV performs much better than expected and is about as efficient as majority voting.

Liang, Philip. A Study of Quadratic Voting. 2020

https://drive.google.com/file/d/1L4XNoO2Vd55qAWeJ5T3k2fBaG0sDGJXl/view