Solid coalition
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. This definition is useful even in the absence of party labels, or when labels do not accurately reflect ideological divisions in the electorate.
Definition
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.Example
Consider the following example, taken from American politics of the 1800s:| Share: | 25% | 30% | 20% | 25% |
| Clay | 2 | 1 | 4 | 3 |
| Webster | 1 | 2 | 3 | 4 |
| van Buren | 3 | 3 | 1 | 2 |
| Jackson | 4 | 4 | 2 | 1 |
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. Similarly, the remaining 45% of voters form a Democratic coalition.
Note that solid coalitions can be nested within each other. For example, the solid coalition consisting only of Jackson has support from 25% of voters. However, there cannot be overlapping, non-nested, solid coalitions. 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.