Minimal Requirements for Representation in the Democratic Primary
Michael A. Jones
Associate Editor
Mathematical Reviews
American Mathematical Society
In the Democratic Party Primary, presidential candidates are assigned
delegates based on their share of the vote in each primary state using
Hamilton's method of apportionment. However party rules state that
candidates receiving less than 15% of the vote are not awarded any
delegates. In this talk, we look at the consequences of such a cut-off
for Hamilton's method and several other apportionment methods. For each
method, we find the threshold of inclusion (the level of support
necessary to possibly receive a delegate) and the threshold of
exclusion (the level of support necessary to assuredly receive a
delegate). We compare these values and determine the relationship
between the thresholds and the Democratic Party cutoff of 15%. We also
examine a new apportionment paradox that can arise when cut-offs are
applied to Hamilton's method.