Arbitrary Democracy

A Weyker-Roca Production

Some definitions...

• Preferences - binary ordering over outcomes (x > y, etc)

• Democracy - not in the public forum sense but in the social will sense (aggregation of everyone’s preferences to make a social preference)

• Dimension - an option space; the further from your ideal option the lesser your preference (left vs right, etc). 

• Outcome – some state of affairs ‘x’ or some other state of affairs ‘y’, etc

Jefferson Defined Democracy as the will of the people.

This is typically how most people see it to.

However we offer a challenge that whether or not democracy is conducted fairly it fails to meet this standard.

What is your ideology?

Marxist, Libertarians, Democrats, Republicans, Green Party, Pansexual Peace Party, Piracy Party, Weed Party, Beer Keg Party

Politics with No Ideology

This philosophy is based on…• Economic reasoning• Assumptions of Homo economicus

o Utility maximizer - you vote to meet your desires• As applied through the means of democracy

o Attempt to express will of the people

To Democracy!

• Axiomatic social choice theoryo I.E. The basic assumptions for democracy

o It seems like you can’t have a voting system without certain rules

o What you need as a minimum for a true democracy.

o Supposedly self-evident conditions (axiom-like)

The conditions for two options...May's Theorem:• Universal Decisiveness- You will get a clear

result• Undifferentiatedness- Your vote matters no

matter who you are.• Neutrality- Nothing can be predisposed to win.• Strong Montonicity- Your vote will always help

and never harm your preferred option. 50%+1 FTW!

Any voting system weighing two options must meet these conditions!!

Simple majority rules (50%+1) uniquely satisfies this.

Problem one...

• Simple majority allows for unique fulfillment of May’s conditions

• What about when three or more options are under consideration?

• Well, let’s try to keep ‘simple majority’ in our new systems

• This is known as the Condorcet Method (there are others with their own problems, as we will see)

The Condorcet Method• Pair up every option with each other, it’s a round-robin (x vs. y; x vs z; z vs y)• Simple majority rules determines each voters’ preferences and reveals their

preference ordering.• This is prone to a ‘paradox’

Notice the circular result! X to Y, Y to Z, Z to X

Alf Betty Charlie

X Y Z

Y Z X

Z X y

Arrow's Theorem...

Arrow Conditions:• Universal Domain: All logically possible options for

(x,y,z)• Pareto Principle: If everyone wants x over y, then

you will get x over y.• Pairwise Independence of Irrelevant

Alternatives. The addition of z, should not effect the relation between x and y.

• Non-dictatorship- No one person can control the outcome    

With these Arrow argues that no voting system can produce a “fair” result.

Problems

• The thought is that given Arrow’s conditions, there is no voting method which can fulfill all of them; they contain a contradiction – except for the Condorcet Method.

• However, we know the Condorcet method is prone to a ‘paradox’• When does this ‘paradox’ occur? How probable is it?

First let’s look at the Condorcet Paradox graphically!! 

No paradox: single peaked preferences

Paradox: transitive result with double peaked preferences

What “drags” Charlie’s peaks around?

Arbitrary Results!!

• Multiple dimensions “drags” Charlie’s preferences!! In other words, brings about the Condorcet Paradox!!

• More dimensions, more probable.o Dimension is an option-space (left vs right, pro-life vs pro-choice, etc)

• With multiple dimensions you can get agenda control o Each question emphasizes a different dimensiono In other words, ask the right questions and you can get whatever result you want.

 

A legislative example…

• Anti-discrimination = x• Federal aid to education = y• Status Quo = z

• Powellians – x>y>z (132)• School Aiders – y>x>z (67)• Southern Dems – y>z>x (130)• Republicans – z>x>y (97)

• First question: bill (just aid) vs. amended (aid + no seg.)

• Second question: amended vs. no bill (status quo)

• The legislative system is easily manipulated due to its built in agenda control!!

An explanation…

So we have the first question which asks us “Federal aid to schools or aid with the condition of no segregation?”The Powellians and School Aiders were for amended bill. The Southern Democrats, who at the time had segregated schools, voted for the original bill. The Republicans strategically voted for the amended bill.

The second question was “Aid and no segregation or status quo (no aid)?”Powellians and School Aiders went for the amended bill, the Southern Dems went for status quo, Republicans switched to status quo.

An explanation…

The first question highlights the dimension of segregation.

The second question highlights the dimension of size of government.

The Republicans saw this an strategically voted to defeat the effort for federal aid!

Thus, the legislative process has built in agenda manipulation!!

Unpopular presidents example

• Over all least popular candidate, yet the winner!

• Also occurred with Lincoln and Clinton

Wilson Roosevelt Taft

42% 27% 24%

Roosevelt Taft Roosevelt

Taft Wilson Wilson

Lessons learned...

• No voting method fulfills all requirements proposed by Arrowo There will always be a problem

• Outcome is fully contingent on how you do the voting• Think of the dimensions which are emphasized by the

media in an election season! • Is it safe to say the media and political parties set the

agenda for the electorate??– Be weary of voting results!!

Recommended reading

• Liberalism Against Populism by William H. Riker; • On Philosophy, Politics, and Economics by Gerald

Gaus;

• And not fully related to the material here, but a good read:

• The Calculus of Consent by James M. Buchanan