Making EVERY Vote Count
The following resources are provided for those who would like to delve deeper into the study of voting systems and include not only the extensive analyses performed by election reform authority Charles T. Munger, Jr., but also others with expertise in the field. If you would like to provide any comments on, or contributions to, these resources, please use the Contact Us section of this website.
Analyses
My various papers each have individual abstracts that gives their principal results, and each has an introduction that describes the content of the separate section of the paper. The papers and sections can (mostly) be read independently of each other; think of a section as something like an entry in an encyclopedia, a book which one could if one chose read from cover to cover, but which is designed to let a reader look up and read information about one topic mostly without reading information about another.
To help a potential reader navigate, here the papers are grouped into one of three categories: The California Top-Two Primary; Condorcet Methods Versus Instant Runoff and Election Methods Without Ranked-Choice Ballots.
For each paper is listed its title, often its abstract or a summary, and then what can be found in it, section by section. Major sections of a paper are indexed by Roman numerals; subsections, by capital letters; and sub-subsections by numbers.
A summary and conclusions covering all three linked papers — California's Top-Two Primary: A Successful Reform, papers I, II, and III — appears in III on p. 13. The four linked papers The right way to read Ranked-Choice ballots: not Instant Runoff, but Ranked Pairs, papers A through D have a single abstract
Dropping one candidate under Beatpath and Ranked Pairs
Summary: We report for Beatpath and Ranked Pairs an exhaustive examination of how the winning candidate changes when one candidate is dropped, for initial numbers of candidates of 4 and 5, and report sampling results of what happens for initial numbers of candidates from 6 to 18. Consistent with all the searches is the observation that if under Beatpath there is a single rank order, and if when the winning candidate drops there is also a single rank order, then in the new rank order the candidate who formerly placed second must place above the candidate who formerly placed third; and therefore we add to the proof by M. Schulze that the candidate who placed second cannot become placed last, the observation that the candidate who placed third cannot become placed first. Other than those two excluded cases, for candidates numbering from 4 to 18 we find that a candidate who placed anywhere in the original rank order could be found to be placed anywhere in the new rank order; in particular the candidate who had placed last could come to be placed first, and the candidate who had placed second could come to be placed second-to-last. These results are compared to the known properties of Ranked Pairs, and their larger political significance discussed.