The Story So Far
- Pure democracy (majority rule) is indeterminate
- Condorcet's Paradox: cycling from 3+ choices, 3+ voters, and disagreement
- Arrow's Impossibility Theorem: no non-dictatorial rule can efficiently and fairly determine a group choice
- Agenda control & strategic voting
The Story So Far
- Democracy devolves into dictatorship or institutions are created to restrict choice
- Constitutional republics: limit domain of what may be voted on
- Real world electoral systems reduce effective choices to 2
- First-Past-The-Post: Duverger's Law ⟹ two political parties
- Parliamentary: "government" vs. "opposition"
The Story So Far
Voters imperfectly vote for a candidate closest to their preferences
Voters have poor incentives (MC>MB) to inform themselves or to vote for the best candidate
- Good governance is a public good with free rider problem
- Rational ignorance
- Rational irrationality
Radical Markets
Eric Posner
Glen Weyl
2018, Radical Markets: Uprooting Capitalism and Democracy for a Just Society
A series of proposals to make markets and democracy more free and efficient, but also more equal and just
- too much inequality and market power right now
Argued economically, often market-like proposals
- mechanism design, game theory
What's Wrong With 1P1V?
The bedrock of democracy is the idea of One person, one vote (1p1v)
- Everyone has equal voice in the outcome
Used to argue for extending the franchise to women, African Americans, etc
Constitution requires representation in Congress apportioned to population
What's Wrong With 1P1V?
Tyranny of the majority: unprotected minorities can get trampled on by the majority
Persistent minorities view system as illegitimate, turn to other means of resistance
- secession, riots, violence
What's Wrong With 1P1V?
U.S. only started protecting a lot of abused minorities in 20th century
Mostly result of federal court cases
- Not very democratic! Unelected, unaccountable life-long judges
- Seem to rely on preferences of judges
Federal troops protecting the "Little Rock Nine" during racial integration of schools.
What's Wrong With 1P1V: Ordinality
Voting systems give equal weight to preferences by person
No way to differentiate preferences or intensities
- Only ordinal rankings: A>B or A<B
An indifferent, lethargic majority, can outvote a passionate minority
Cardinality: In Markets
In markets, not only more choices, but can indulge intensity of your preferences
If you want 4 more cookies, you can buy 4 more cookies
Goods flow to those that value them the most, willing to pay the most
From Markets to Politics
But we can't easily transfer market mechanisms to collective choices
Free rider problem of voting and informing oneself
Voters with the strongest preferences can just try to "buy" the most votes
From Markets to Politics
Olson: smaller, more passionate groups can better organize than large, apathetic groups
- most people don't know (or care) about bank regulation, nuclear power, emissions standards
- rational ignorance
Special interest groups have a strong incentive to capture the democratic process
- rational: high level of participation
Getting the Price Right
- In markets, the cost of acquiring more goods is proportional to how much you want them
- Again, for 4 more cookies, pay 4x the price of one
Getting the Price Right
William Vickrey
1914-1996
Economics Nobel 1996
Work on auctions and auction theory
Auction's goal: get item to the person who values it the most
Getting the Price Right
William Vickrey
1914-1996
Economics Nobel 1996
Turns out, more important to get the winner to pay the price that compensates for the cost that they create
- Other bidder cannot get the item
Vickrey or Second-price auction: Winner pays the bid of the second-highest bidder
Markets, in general: prices reflect opportunity cost of next best alternative use
- What somebody else is willing to pay for a different use
Getting the "Voting Price" Right: A Hypothetical for Intuition
- Suppose society votes to zone land for cattle ranching, optimum at A
Getting the "Voting Price" Right: A Hypothetical for Intuition
Suppose society votes to zone land for cattle ranching, optimum at A
But more ranching imposes a cost on Farmer Frank (Cows eat his crops)
Without Frank, optimal ranching is at A.
But with him, social cost increases, moving social optimum back to B.
Getting the "Voting Price" Right: A Hypothetical for Intuition
In some sense, Frank imposes an externality on society for reducing its ranching from A to B
Frank should have to "pay" for the additional external cost imposed, which is the area of the DWL triangle
Getting the "Voting Price" Right: A Hypothetical for Intuition
What if the cost to Frank is actually larger?
Area of DWL triangle grows in size with the square of the reduction in quantity
More valuable land (higher MSB) is prevented from becoming farmland
- Value of lost farmland is increasing as more farmland is being lost!
From Prices to Votes
But this ruling is going to be determined by votes, not market prices or transactions
Under 1p1v, marginal cost of "buying" votes is constant
Those that care very much try to buy all the votes
- Cost per vote to them is too low
Those that don't care very much
- Cost per vote to them is too high
From Prices to Votes
- Posner & Weyl's proposal: "Quadratic Voting"
What if people could "buy" votes to spend on an issue
The total cost of buying votes should increase quadratically
- i.e. cost of n votes is n2; or
- most votes you could buy with x is √x
Proposed Benefits of Quadratic Voting
Get a better indication of people's preferences
Reduces strategic voting, cycling, free-rider problem
More of an incentive to inform oneself - have one's votes count proportionate to degree of interest
A passionate minority can now outvote an indifferent majority
- Is that what we want??
How Might it Work?
Imagine each person is given a budget of "voice credits" Q per year (e.g. 100 Q)
For each issue, individual can expend x Q-credits to cast √x votes
Q-credits "rollover" if not spent on issues
Can save credits for issues you care more about
Screenshot from "Collective Decision Engines"
How Might it Work?
Each person can cast as many votes as desired FOR and AGAINST any proposal
If total votes For > total votes Against, resolution passes (and vice versa)
Screenshot from "Collective Decision Engines"
How Might it Work?
- Multiple option voting:
- Have a default option
- People can cast as many votes FOR and AGAINST as many options as they want
- If any option gets the most votes, enacted
- If no option gets most votes, default option enacted
Screenshot from "Collective Decision Engines"
Interest in Quadratic Voting Beyond Politics
