'Voting power' has several meanings. The interested reader can find a systematic critical examination and exposition of these in the monograph by Dan Felsenthal and Moshé Machover The Measurement of Voting Power: Theory and Practice, Problems and Paradoxes (Cheltenham, UK: Edward Elgar, 1998).
Under all its meanings, voting power is concerned with a collective body (assembly) whose members decide by yes/no vote whether to adopt a proposed resolution. The decision rule (also known as 'voting game') under which the assembly operates specifies whether any particular proposed resolution can at all be put to a vote and, if put to a vote, what kind of support it must have among the assembly's members in order to pass. An assembly can use various decision rules for voting on various kinds of proposed resolution.
We first distinguish between a priori (or de jure) and a posteriori (or de facto) voting power.
The a priori voting power of a voter within the assembly (who can be a single individual or a bloc of individuals acting as a single person), is the extent that this voter can control the outcome of the voting merely through the resources made available to this voter by the decision rule.
In contrast, assessment of a voter's a posteriori voting power ought to take into account additional relevant resources that may be available to this voter, such as rhetorical persuasiveness, bargaining ability, prior bias regarding the issues voted upon, and affinity or disaffinity between him/her and other voters. In order to measure a voter's past de facto voting power during a certain period of time, one would need data on how all voters have voted and the final outcome of all divisions that occurred during that period. Such data are often available. However, current and future de facto voting power requires mathematical modelling of voter's preferences, affinities etc. - a task that poses difficult and controversial theoretical and empirical problems.
Most of the research to date on voting power has concentrated on a priori voting power. This type of voting power can be divided into two sub-types dubbed by Felsenthal and Machover (op. cit.) I-power and P-power.
A priori I-power is the degree to which a given voter is able to influence the outcome of the vote, ie whether the proposed resolution will pass or fail. A voter's I-power, as first defined by Lionel Penrose in 1946, is measured by the probability that s/he will be decisive given the decision rule, and assuming that all voters vote independently of one another, and that every voter supports or opposes a proposed resolution with equal chance.
The relative I-power of a given voter, known as the voter's Banzhaf index is equal to the absolute I-power of that voter divided by the sum of absolute I-powers of all voters.
Several alternative I-power indices have been proposed in the literature, but they all suffer from various theoretical deficiencies.
The second sub-type of a priori voting power, that of P-power, views the ultimate outcome of the voting process as the distribution of a fixed purse - the prize of power - among the victors, eg the distribution of cabinet portfolios among the members of a governmental winning coalition. From this viewpoint, a voter's (relative) voting power, the extent of his or her control of the ultimate outcome, is usually defined as that voter's expected or estimated share in the fixed purse. Since so far no completely satisfactory solution has been found to the n-person bargaining problem, there exists no undisputed measure for P-power. The measure commonly used in the literature to assess a voter's P-power is the Shapley-Shubik index.