Spatial Voting Models: A Dynamical Systems Approach
Bibliographic record
Abstract
Spatial voting models have been used extensively to study factors affecting candidate positioning in elections. Most previous research has fixed candidate positioning at one point in time to determine optimal candidate payoff. In this paper we examined candidate positioning within a dynamical system, thereby adding a temporal component to the analysis that allowed for a more realistic model of candidate behaviour in the lead-up to an election. Using a two-candidate and one-voting bloc case, the results from this research identified several critical points that described different types of candidate equilibria. Competitive critical points mirrored findings in previous research. Flip-Flop and Noncompetitive points, however, identified sub-optimal candidate positions that might arise during an election. Flip-flop points appeared to highlight situations in which candidates oscillated between trying to outmaneuver their opponent and attempting to move closer to their ideological positions. Noncompetitive points seemed to describe candidate intransigence regarding their policies. Bifurcation analysis revealed how the dynamical system was affected by subtle differences in the voting bloc’s position. We also examined the relationship between the Nash equilibrium solution concept and asymptotic stability of critical points. Although our findings suggested that Nash equilibrium points are always asymptotically stable critical points, the converse was not necessarily true. Future studies might extend this spatial voting model by increasing the number of candidates or weighting the voting blocs to see how these changes affect the dynamics. Additional research could also investigate whether it is true that an asymptotically stable critical point with complex eigenvalues is never a Nash equilibrium point in all dynamical systems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".