Condorcet Counter
This is a simple excuse to play with Scala Native and some Condorcet algorithms.
Prerequisites
Requires Boehm garbage collector and the RE2 regular expression library installed natively. See scala-native docs for details.
Usage
This is a simple script designed to be run from the shell. It first prompts for the list of candidates starting with id 1:
1: Teddy Roosevelt
2: Ned Stark
3: Sauron
Hit Control-D to continue. Then it prompts for the list of ballots:
3:1>2>3
5:2>1=3
1:3>2>1
The first number is the number of ballots with that preference
order, and the part after the colon is the preference order.
Ties are allowed via the = sign.
The output is the complete order of candidates, grouped by Schwartz and Smith set. This is accomplished by finding the set, removing those candidates from the ballots, and recounting until a complete order is calculated.
Condorcet Discussion
For a brief review, a Condorcet Winner is a single candidate that
would beat all other candidates head-to-head. A Weak Condorcet Winner is a single candidate that would beat or tie all other
candidates head-to-head.
The Smith Set is the smallest set of candidates that would beat all
other candidates head-to-head.
The Schwartz Set is comprised of candidates that would beat or
tie all other candidates head-to-head.
A single-candidate Smith Set is a Condorcet Winner. A single-candidate Schwartz Set is at least a Weak Condorcet Winner.
There are many other algorithms that purport to elect a single winner from a multi-candidate Smith Set or a Schwartz Set. The literature at this point is deeply misleading, as the flaws with these "tie-breaking" algorithms are often painted as flaws with Condorcet methods in general.
Complicating this is that several so-called "Condorcet Method" algorithms entirely skip the identification of the Smith or Schwartz sets, in favor of identifying a single winner even if there isn't a Condorcet Winner. This contributes to the confusion in the literature.
A multi-candidate set often (but not always) indicates a preference cycle, and it is impossible to fairly select a single winner from a preference cycle. But this is not the fault of the Smith/Schwartz Set. "The fault, dear Brutus, is not in our stars / But in ourselves". It is the electorate itself that has this inconsistency.
It's this author's view that a method should only be called a Condorcet Method if it is limited to identifying the Smith Set, or the Schwartz Set if Weak Condorcet Winners are allowable.
All other so-called "Condorcet Completion" algorithms should be described as they are - tie-breakers that are by their very nature flawed, in that they try to force consistency on a set of ballots that is by definition not consistent.
For elections that are willing to accept these risks and flaws in the count, this is of course allowable. But for those that wish to find a true Condorcet Winner, the appropriate remedy is to identify the Smith or Schwartz set, allow the electorate further time to discuss and decide, and then hold additional rounds of elections restricted to those candidates in each round's Smith or Schwartz set, until a single winner is identified.