Optimisation and game theory · Maths EE idea · Ambitious

Can any voting system be fair?

A research question to start from

Which fairness conditions do plurality, Borda and instant-runoff voting satisfy, and why can no ranked system satisfy all of Arrow's conditions?

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Why it works as a maths EE

Precise definitions, counterexamples you construct and a famous impossibility result.

Mathematics you would need

Preference profiles
Logical conditions
Counterexample construction
Proof of Arrow's theorem (or a simpler version)

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Define each fairness condition precisely.
Construct profiles that break each system.
Prove a simplified version of Arrow's theorem and explain the full one.

Scope and difficulty

Ambitious. Ambitious.

Pitfalls

Politics essay.
Conditions left vague.

Where to start reading

Search a library catalogue or a university's open lecture notes for: Arrow impossibility theorem proof simple; Borda count violations independence. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.