The Banzhaf Fallacy
Bibliographic Data
| ID | 6231854 |
|---|---|
| Authors | Howard Margolis (corresponding author) |
| Year | 1983 |
| Volume | 27 |
| Issue | 2 |
| Pages | 321 |
| Publication date | 1983-05-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | American Journal of Political Science (JOURNAL) |
| Journal identifiers | ISSN: 0092-5853 • E-ISSN: 1540-5907 |
| Publisher | JSTOR (PUBLISHER) |
| DOI | 10.2307/2111020 |
| OpenAlex | W2333211982 |
| Language | EN |
| Citations received | 15 |
| References cited | 2 |
According to a frequently published argument (which I will label the Banzhaf argument) there is an intrinsic, large-state advantage in presidential elections, proportional to the square root of the relative size of the state. If the argument were empirically meaningful, its proponents have always implied and usually asserted, then a voter in California would enjoy about twice the voting power of a voter in Virginia (reflecting the roughly fourfold ratio in population). This advantage, moreover, is presented an intrinsic mathematical property of the electoral college scheme, not something deduced from demography, voting patterns, or some other appeal to empirical observations. The earliest versions of the argument are Banzhaf (1968) and Riker and Shapley (1968). Subsequent variants of the argument can be found (among other places) in Brams and Davis, 1974, Owen, 1975, and Lake, 1979. With the obvious exception of Arrow's Impossibility Theorem, there cannot be many mathematical arguments more often cited by nonmathematical political scientists. However, when mathematical analysis produces a counterintuitive result, it is prudent to allow for the possibility that what needs to be corrected is the mathematics. Brian Barry has made this point in a recent discussion of indices of voting power (Barry, 1980). As it happens, the particular voting power index we are considering here provides a very striking illustration of Barry's message. A preliminary point of the discussion that follows is that the Banzhaf argument depends on a treatment of elections (for purpose of calculating a power index) as if they were like experiments in coin tossing, each voter tossing a coin to decide whether to vote Democratic or Republican. Of itself, the unrealism of the coin-tossing model does not make the Banzhaf result a fallacy, because all models use some more or less unrealistic simplifying assumptions (even in the natural sciences), and even extremely artificial assumptions occasionally produce adequate approximations of real situations
Argument (complex analysis · Counterintuitive · Epistemology · Fallacy · Impossibility · Mathematical economics · Physics · Political science · Politics · Population · Power (physics · Sociology · Voting · Demography · Electoral Systems and Political Participation · Game Theory and Voting Systems · Law · Mathematics · Media Influence and Politics · Philosophy
On the Theory of Strategic Voting1
What Voting Power Cannot Be
Banzhaf voting power, random elections, and the Electoral College winner’s advantage
Pivotal states in the Electoral College, 1880 to 2004
Influence versus utility in the evaluation of voting rules
Why the Electoral College is good for political science (and public choice)
Cognitive biases in moral judgments that affect political behavior
The U.S. Electoral College and Spatial Biases in Voter Power
A State-Level Policy Change That Would Revitalize the Electoral College
The Power of the States in U.S. Presidential Elections
Politics, Economics and the Measurement of Power
Why You Should Vote to Change the Outcome
Political Action Versus Voluntarism in Social Dilemmas and Aid for the Needy
The electors shall meet in their respective states
How we count counts
| Unique citing works | 15 |
|---|---|
| Citations per year | 0.38 |
| Citation span | 1986 - 2025 (40) |
| Citation velocity | recent |
| Highly cited | No |
| Citation types | Neutral: 15 |