Electoral systems & party/seat maps #

Duverger’s law (plurality in single‑member districts → two effective parties, via mechanical + psychological effects). ( Wikipedia)
Micromega rule (“the large prefer the small; the small prefer the large” institutions), incl. its link to party incentives and SPM. ( Wikipedia)
Cox’s M+1 rule (in an M-seat district, equilibrium yields ≤ M+1 viable candidates; formalized for SNTV). ( Cambridge University Press & Assessment, JSTOR)
Cube rule (cube law) (FPTP seat–vote elasticity ~ cubic in two‑party settings). ( Wikipedia)
Seat‑product model (SPM) (expected effective number of parties N≈(M·S)^{1/6}). ( Wikipedia)
Cube‑root law of assembly size (assembly size ≈ population^{1/3}). ( Wikipedia)
Penrose square‑root rule (voting weights ∝ √population to equalize citizen power). ( Wikipedia)
Second‑order election theory (EP elections behave as “second‑order” to national contests). ( Wikipedia)
Effective number of parties (Laakso–Taagepera) (ENP as an inverse‑HHI; widely used). ( Wikipedia)

Arrow’s impossibility theorem (no SWF meets UD+IIA+Pareto+non‑dictatorship for ≥3 options). ( Stanford Encyclopedia of Philosophy, Wikipedia)
Gibbard–Satterthwaite theorem (every resolute ordinal single‑winner rule with ≥3 options is manipulable or dictatorial). ( Wikipedia)
Duggan–Schwartz theorem (for set‑valued rules, strategy‑proofness + mild surjectivity ⇒ weak dictatorship / manipulability). ( Wikipedia)
May’s theorem (majority rule uniquely satisfies anonymity, neutrality, and positive responsiveness for two options). (Overview) ( Stanford Encyclopedia of Philosophy)
Condorcet jury theorem (under independence and p>0.5, majority accuracy → 1 as n grows). ( math.chalmers.se)

Legislatures, coalitions, and agenda power #

McKelvey–Schofield chaos theorem (in multidimensional policy spaces, majority rule is generically unstable; agenda control can reach almost any point). ( Wikipedia)
Riker’s size principle (coalitions tend to be minimal winning under standard assumptions). ( Wikipedia)
Veto player theory (Tsebelis) (more veto players/greater ideological spread ⇒ higher policy stability). ( Wikipedia)
Pivotal politics (Krehbiel) (gridlock and lawmaking hinge on pivotal legislators relative to filibuster/veto pivots). ( University of Chicago Press)

Iron law of oligarchy (Michels) (organizational tendencies toward oligarchic control). ( Wikipedia)
Selectorate theory (Bueno de Mesquita et al.) (incentives from selectorate vs. winning coalition sizes). ( Wikipedia)
May’s law of curvilinear disparity (party activists more extreme than voters and leaders). ( Wikipedia)
Democratic peace (empirical regularity) (mature democracies rarely fight each other; various mechanisms posited). ( electowiki.org)

Holmström (1979) “informativeness principle” (any signal informative about action should enter optimal contracts). ( Duke People, NBER)
Holmström (1982) “moral hazard in teams” (team production ⇒ free‑riding; budget‑balance typically incompatible with first‑best incentives). ( Duke People, JSTOR)
Myerson–Satterthwaite theorem (bilateral trade with private values cannot be efficient, budget‑balanced, IR, and IC simultaneously). ( Wikipedia)

DeGroot learning (iterated weighted‑average updates converge to a consensus weighted by eigenvector centrality under connectivity/aperiodicity). ( Wikipedia)
(Related pointers) Mathematical models of social learning overview; information cascades. ( Wikipedia)