A formal framework that represents voters’ and candidates’ policy preferences as points in one or more ideological dimensions and predicts electoral choices by proximity (policy distance) between voters’ ideal points and candidates’ positions under defined decision rules.

Principle

Under proximity decision rules, voters choose the candidate whose position minimizes policy distance from their own; in single‑dimensional, deterministic settings with vote aggregation, strategic incentives can drive candidate convergence toward the median voter, conditional on assumptions about information, turnout, and issue salience.

Demonstration

Illustrative scenario → On a left–right economic axis, two major candidates choose platforms; given voters’ left–right ideal points, those nearer to a candidate are predicted to vote for her, and if both seek to maximize votes, each has an incentive to move toward the median voter position under the model’s assumptions.

Misapplication

Applying unidimensional proximity logic to contexts with salient multiple issue dimensions, strong valence factors, or identity cues is a category error; the semantic mistake is to treat policy distance as the sole determinant of choice when non‑policy attributes matter.

Consequence

The model yields testable predictions about candidate positioning, policy convergence or divergence, and the effects of dimensionality and strategic entry on electoral outcomes; it clarifies when policy moderation is a strategic equilibrium and when multidimensionality permits persistence of distinct platforms.

Reversal

If voters rely on non‑policy information (valence, competence), if turnout or entry constraints distort median incentives, or if issue dimensionality is multi‑axial and salient, the simple proximity predictions (including median convergence) fail or require qualification.

Boundary

Clearly within: contexts where voters’ policy preferences are expressible along continuous ideological scales and policy dimensions drive choice.Boundary case: systems with a dominant dimension plus salient secondary dimensions where proximity partially predicts behavior.Clearly outside: choices driven primarily by identity, clientelism, or valence attributes unrelated to policy distance.

Semantic Tension

Proximity ↔ Valence/Identity — distance‑based spatial explanations compete with valence models (competence, integrity) and identity‑based accounts; empirical application must adjudicate which factors dominate in a given context.

Synthesis

The spatial model supplies a geometric apparatus to map preferences into choices and to derive equilibrium strategies, but its empirical usefulness depends on correctly specifying dimensionality, decision rules, and the relative salience of policy versus non‑policy cues.