Allocation, Ranking & Bargaining Models

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Abstractions about how agents are ranked, matched, or allocated shares, covering matching and fair-division problems (stable roommates problem, individual-pieces set), bargaining and coalition models (Rubinstein bargaining model, strong Nash equilibrium), ranking and vote-counting rules (standings, dot-voting, ballot exhaustion), and unequal positions (bid rent, class stratification).

11 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Ballot Exhaustion — A ranked ballot becomes inactive in a count when its markings supply no valid vote for any continuing candidate.
• Bid Rent Theory — A spatial land-market model in which users' location-dependent maximum bids determine idealized rents and land uses.
• Class stratification — A social-structural ordering in which populations occupy unequal and partly durable class positions through differential access to wealth, income, productive assets, education, status, authority, security, and political power, together with institutions that reproduce or alter mobility.
• Dot-Voting — A more common and slightly more complex cumulative voting system is called dot voting or multi-voting.
• Fair Division — The formal allocation problem of assigning goods or burdens among agents under an explicitly stated fairness criterion and feasible-share constraints.
• Gig economy — A labor-market arrangement in which organizations or customers purchase bounded tasks or short engagements from workers—often mediated and governed by digital platforms—rather than providing continuous standard employment.
• Individual-Pieces Set — In fair cake-cutting, the set of all utility vectors attainable by partitions of the cake among named agents; its boundary exposes feasible and Pareto-efficient allocations under declared valuations.
• Rubinstein bargaining model — An infinite-horizon alternating-offers bargaining game whose unique subgame-perfect division reflects the players' discounting and first-mover position.
• Stable Roommates Problem — A matching problem on an even-sized, non-bipartitioned set in which every participant strictly ranks every other participant and a solution is a perfect pairing with no blocking pair; unlike stable marriage, a solution need not exist.
• Standings (sports) — In sports, standings, rankings, or league tables group teams of a particular league, conference, or division in a chart based on how well each is doing in a particular season of a sports league or competition.
• Strong Nash equilibrium — A strategy profile from which no coalition can jointly deviate so that every coalition member becomes strictly better off.