Choice Theory and Voting Paradoxes

Key ideas#

No universal theory of choice#

Choice problems differ by the number of alternatives, the type and number of criteria, the number of decision makers and how far they agree, the kind of uncertainty, whether the choice repeats, and who bears the consequences. Combining these factors, Tarasenko counts around 800 distinct kinds of choice problem. Expect to pick a method, not apply “the” method.

One criterion#

With certain outcomes, the best option simply maximizes the criterion. That is easy to state and can be hard to compute; it is the field of optimization.

Many criteria: the Pareto approach#

Collapsing many criteria into one (weighted sums, fixing all but one criterion, lexicographic ordering, aspiration levels) always adds an arbitrary element: someone chose the weights or the order. The sounder approach is Pareto’s:

• Option A dominates B only if A is at least as good on every criterion and better on at least one.
• If A wins on one criterion and B on another, they are incomparable.
• The options no one dominates form the Pareto set. That set is the honest answer to a multi-criteria problem. Choosing within it takes a judgment call by the decision maker, chance, or an extra criterion.

To choose within the Pareto set, Tarasenko describes the even swaps method of Hammond, Keeney and Raiffa. Build an options-by-criteria table, remove dominated options, drop criteria on which the remaining options are equal, then trade a change on one criterion for an equivalent change on another until one option, or one criterion, remains.

Pairwise comparison#

When no criteria can predict the outcome (you cannot pick a boxing champion by weighing the boxers), compare options head to head and draw a preference graph. The number of pairs grows roughly with the square of the number of options, so in practice you use shortcuts such as groups or knockout rounds.

Seven paradoxes of group choice#

A group decision is computed from individual preferences by some procedure, and no procedure is free of surprises:

1. The group is not always right. Voting coordinates action; it does not establish truth.
2. No decision is possible. Any threshold, from simple majority to consensus, can fail to be reached.
3. Condorcet’s paradox. Three voters ranking A>B>C, B>C>A and C>A>B produce a cycle; the winner depends only on the order of the pairwise votes.
4. A minority can win under majority rule through low turnout, a split vote, or multi-stage voting.
5. A large majority is not the same as fairness. A rule that looks very inclusive can still be used to redistribute resources against a minority. What protects people is safeguarding minority interests and basic rights when decisions are carried out, plus the chance to correct mistakes at the next vote.
6. Unanimity has traps. It is the only rule that lets everyone defend their interests, but “nobody objected” is easily passed off as “everybody agreed”, and pressure for unanimity breeds groupthink. When agreement is missing, widen each side’s acceptable range (compromise) or take a ladder of small unanimous steps.
7. Arrow’s impossibility theorem. A few reasonable fairness requirements for a voting procedure (no dictator, monotonicity, independence from irrelevant alternatives, any outcome possible) cannot all hold at once. Only collective choice can end in no decision, so you always trade democracy against a guaranteed result.

Decisions in organizations#

Tarasenko argues that a decision belongs at the level of the hierarchy that holds the most information about the problem, often not the top, which justifies delegation and a participative style. He also quotes Ackoff’s definition of a bureaucrat: someone who can say “no” but not “yes”, because in a hierarchy a refusal is rarely counted as an error and an approval can be.