Solid coalition

Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results In social choice theory, a solid coalition or voting bloc is a group of voters who support a given group of candidates over any opponent outside the group.

Solid coalitions formalize the idea of a political faction or voting bloc, allowing social choice theorists to study how electoral systems behave when there are ideological divisions, without having to make explicit reference to political parties.

A solid coalition is a group of voters N together with some set of candidates C such that each voter v in N prefers all candidates in C to all candidates outside of C. Consider the following example, taken from American politics of the 1800s: In this election, the Whig faction creates a solid coalition with 55% of the vote, because 55% of voters rank both Clay and Webster over both van Buren and Jackson.

This fact underlies the tendency of systems like the single transferable vote to become disproportional when voters are not cleanly divided into homogenous political parties, but instead face cross-cutting cleavages (as can happen if racial and ethnic groups do not consistently vote for the same party).

One important use of solid coalitions is in defining proportional representation systems that do not rely on party labels.