Left, Center, Right

Left, Center, Right, or LCR for short, is a type of election scenario that is useful for demonstrating center squeeze and that House monotonicity is incompatible with the Condorcet and Droop proportionality criteria.

The pattern of the scenario is as follows:

x: L>C>R
y: R>C>L
z: C>L>R or C>R>L

where x + y makes up a majority of the voters, but neither the x or y bloc is a majority on its own. It is furthermore common that x > y > z, and the z bloc votes C>R>L, so that L is the Plurality winner and R is the IRV winner; but, depending on what is being demonstrated, that is not necessary.

The scenario was first referenced by Juho.

Center squeeze

See also: Center squeeze

C is "everybody's second choice", and so is the Condorcet winner, but methods that are susceptible to center squeeze will elect either L or R. Plurality elects either L or R, and instant-runoff voting (and Carey) fails to detect C's broad support and eliminates the center early. Descending Acquiescing Coalitions and DSC are also sufficiently similar to Plurality to fail.

Criterion incompatibility

The Condorcet criterion requires that C is elected in the single-winner case. If x > y > z and both x and y exceed a third of the voters, then the Droop proportionality criterion requires that L and R are elected in the two-seat case. Thus the set of winners for one seat and for two seats are disjoint, which contradicts house monotonicity.