Discrete Math Sections 4.1 & 4.2 (Apportionment & Hamilton's)

Front

What is the main goal of apportionment in discrete mathematics?

Back

To fairly distribute a fixed number of identical objects (like seats) among different parties (like states) based on a proportionality criterion.

Front

Define 'proportionality criterion' in the context of apportionment.

Back

A rule or standard used to determine how to allocate resources or seats among parties based on their relative sizes or populations.

Front

What are the 'N parties' in an apportionment problem?

Back

The groups or entities (such as states) among which the identical objects (like seats) are being distributed.

Front

What is the 'standard quota'?

Back

The standard quota is the number of seats each party would receive if the total number of seats were distributed exactly in proportion to their populations.

Front

What is the 'upper quota'?

Back

The upper quota is the highest whole number of seats that a party can receive, rounded up from the standard quota.

Front

What is the 'lower quota'?

Back

The lower quota is the lowest whole number of seats that a party can receive, rounded down from the standard quota.

Front

Explain Hamilton's Method of apportionment.

Back

Hamilton's Method involves calculating the standard quotas for each party, assigning each party their lower quota, and then distributing any remaining seats based on the largest fractional parts.

Front

What is a 'surplus seat' in apportionment?

Back

A surplus seat is an additional seat that remains after each party has received their lower quota, which can be distributed based on fractional parts.

Front

How do you calculate the standard quota for a party?

Back

The standard quota is calculated by dividing the population of the party by the total population and then multiplying by the total number of seats available.

Front

What is the significance of the fractional part in apportionment?

Back

The fractional part determines how surplus seats are allocated among parties, with those having the largest fractions receiving additional seats first.