Strategic Candidate Nomination – Which Party Has a Chance to Win?
Ildikó Schlotter
In a study performed together with Katarína Cechlárová from P.J. Šafárik University (Košice, Solvakia) and presented at AAMAS 2025, we explore a model where political parties can strategically nominate candidates to influence election outcomes—specifically, under Condorcet-consistent voting rules. These are voting systems that always select the Condorcet winner, a candidate that would defeat every other candidate in a one-to-one comparison, if such a candidate exists.
The Scenario:
Imagine several political parties, each with a shortlist of potential candidates for the upcoming election. Deciding which candidate to nominate is often a complex process that takes into account not only voters’ preferences but also the possible nomination strategies of other parties who plan to participate in the election. Even in a model where parties have full knowledge of how voters rank all potential candidates, finding an optimal nominee for a given party leads to very hard computational problems. Therefore, we focussed on a simpler question that is called the Possible President problem:
Can a given party, say party P, nominate one of its potential candidates so that it has a chance to become a winner? In other words, is there some combination of nominations chosen by the other parties that results in P’s nominee winning the election under the given voting rule?
Our Methodology:
While it is theoretically possible to check every combination of nominations to obtain an answer to the Possible President problem, doing so quickly becomes infeasible as the number of candidates and parties grows. To address this, we investigated the computational complexity of the Possible President problem for a range of Condorcet-consistent voting rules, namely, the Maximin and Copelandα rules (where α is a parameter between 0 and 1). We also studied how the difficulty of solving the problem changes depending on various factors such as
• the number of voters,
• the number of parties, or
• the maximum number of potential candidates affiliated with a given party.
Our Findings:
We provided a full classification of the parameterized complexity of the Possible President problem, analyzing the Maximin voting rule and the family of Copelandα voting rules and thus extending our previous work dealing with positional scoring rules. Notably, we found that the problem remains computationally hard even if each party has only two candidates to choose from, and there are just four voters (or three, when using Copelandα rules). However, there is good news for some scenarios. For election systems using the Maximin voting rule, if the number of participating parties is small, then the problem can be solved efficiently by a fixed-parameter tractable algorithm. This result may lead to practical computational tools for strategic candidate nomination in smaller or more controlled election settings.
Candidate Nomination for Condorcet-Consistent Voting Rules
Ildikó Schlotter – Katarína Cechlárová
AAMAS proceedings published by the International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
AAMAS 2025, May 19 – 23, 2025, Detroit, Michigan, USA
