House monotonicity criterion
The House monotonicity criterion is a criterion for apportionment/party list methods, and by extension, for multi-member methods in general. The term was first used by Balinski and Young in 1974.[1]
The house monotonicity criterion for a Party list method is:
If the number of seats increases with fixed populations, then no party can have its number of seats decrease.
That is, a state must never lose a seat from the number of total seats increasing. The Alabama paradox is an example of a house monotonicity failure.
By extension, the house monotonicity criterion for a Multi-Member System is:[2]
If only the seat count is increase then the Winner set must include all prior winners
House monotone multi-member methods are sometimes called proportional orderings or proportional rankings[3], and James Green-Armytage's Proportional Ordering is such a method. Sequential methods without deletion steps, such as sequential Ebert and sequential Phragmén, are also house monotone.
Related
References
- ↑ Balinski, M. L.; Young, H. P. (1974-11-01). "A New Method for Congressional Apportionment". Proceedings of the National Academy of Sciences. Proceedings of the National Academy of Sciences. 71 (11): 4602–4606. doi:10.1073/pnas.71.11.4602. ISSN 0027-8424.
- ↑ Woodall, D. (1994). "Properties of preferential election rules". Voting matters (3): 8–15.
- ↑ Markus Schulze (2011-03-14). "Free Riding and Vote Management under Proportional Representation by the Single Transferable Vote" (PDF). p. 42.