Malapportionment Index

The Malapportionment Index captures how unequally legislative seats are distributed relative to population across electoral districts. The most widely cited version is the formulation by David Samuels and Richard Snyder (2001), which adapts the Loosemore–Hanby disproportionality index: it sums the absolute differences between each district's seat share and its population (or registered voter) share, then divides by two. The result ranges from 0 (perfect apportionment) to 1 (maximum malapportionment), and is often reported as a percentage.

A score of 0.05 means roughly 5% of seats would need to be reallocated to achieve population parity. Samuels and Snyder's cross-national study of 78 countries found that federal systems and upper chambers tend to be substantially more malapportioned than unitary systems and lower chambers, with the U.S. Senate, Argentine Senate, and Brazilian Chamber of Deputies among the most malapportioned legislatures in democracies.

The index is sensitive to several methodological choices:

• Population vs. eligible voters vs. registered voters as the denominator
• Treatment of at-large or national-list seats (usually excluded)
• Whether upper and lower houses are measured separately or combined

Malapportionment is conceptually distinct from gerrymandering: the former concerns unequal district magnitudes or population sizes, the latter concerns the manipulation of boundaries for partisan advantage. It is also distinct from electoral disproportionality (e.g., the Gallagher index), which measures the gap between vote shares and seat shares at the party level rather than the district level.

Researchers use the index to study rural over-representation, the durability of authoritarian-era district maps, and the bargaining power of small subnational units in federations. In comparative politics it is frequently invoked to explain why redistributive policy or constitutional reform stalls in systems where overrepresented districts can veto change.