The stability set as a social choice correspondence

Abstract We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We focus on the relations between several extensions of the condition of independence of irrelevant alternatives on one hand, and conditions on the revealed preference relation on sets, notably the weak axiom of revealed preference, on the other hand. We also establish the connection between the condition of independence of irrelevant alternatives and so-called strong sets; the latter characterize a social choice correspondence satisfying independence of irrelevant alternatives.

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Characterising scoring rules by their solution in iteratively undominated strategies

Economic Theory ◽

10.1007/s00199-021-01353-w ◽

2021 ◽

Author(s):

Christian Basteck

Keyword(s):

Monotonicity Property ◽

Scoring Rules ◽

The Other ◽

Approval Voting ◽

Property A ◽

Borda Rule ◽

Scoring Rule ◽

Direct Mechanism ◽

Social Choice Correspondence ◽

Choice Correspondence

AbstractWe characterize voting procedures according to the social choice correspondence they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In a larger class of rules, Approval Voting is characterized by a single axiom that implies both U and MEW but is weaker than Condorcet-consistency (CON)—it is the only direct mechanism scoring rule that is majoritarian after eliminating a Pareto-dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected); among all finite scoring rules that satisfy MEPD, Approval Voting is the most decisive. However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). There exists no direct mechanism scoring rule that satisfies both MEPD and MON and no finite scoring rule satisfying CON.

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Pluralism and Social Choice

American Political Science Review ◽

10.2307/1957271 ◽

1983 ◽

Vol 77 (3) ◽

pp. 734-747 ◽

Cited By ~ 73

Author(s):

Nicholas R. Miller

Keyword(s):

Social Choice ◽

Choice Theory ◽

Social Choice Theory ◽

Political Process ◽

Decision Rules ◽

Political Systems ◽

Political Preferences ◽

Normative Criteria ◽

The Stability ◽

Generic Instability

Pluralist political theory identifies certain patterns of political preferences as promoting the “stability” of democratic political systems and others as threatening to such stability. Social choice theory likewise identifies certain patterns of political preferences as leading to “stability” in social choice under majority rule and related collective decision rules, and other patterns as leading to “unstable” social choice. But the preference patterns identified by pluralist theory as promoting stability are essentially those identified by social choice theory as entailing instability. Thus the notions of stability and the implicit normative criteria associated with the two theories are very close to being logically incompatible. This incompatibility suggests that the social choice ideal of collective rationality may not be one that we should endorse. Indeed, the generic instability of the pluralist political process and its consequent collective irrationality may contribute to the stability of pluralist political systems.

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Open discussion

Symposium - International Astronomical Union ◽

10.1017/s0074180900029533 ◽

1982 ◽

Vol 99 ◽

pp. 605-613

Author(s):

P. S. Conti

Keyword(s):

Buenos Aires ◽

Large Mass ◽

List Type ◽

Common Phenomenon ◽

Open Discussion ◽

The Stability ◽

Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

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Symmetric Multistep Methods Revisited: II. Numerical Experiments

International Astronomical Union Colloquium ◽

10.1017/s0252921100031602 ◽

1999 ◽

Vol 173 ◽

pp. 309-314 ◽

Cited By ~ 3

Author(s):

T. Fukushima

Keyword(s):

Multistep Methods ◽

Computational Time ◽

Integration Time ◽

Implicit Methods ◽

Symmetric Methods ◽

Celestial Bodies ◽

The Stability ◽

Predictor Corrector ◽

Symmetric Multistep Methods ◽

Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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Uniformity of Magnification from Different Electron Microscopes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100060179 ◽

1967 ◽

Vol 25 ◽

pp. 32-33

Author(s):

Godfrey C. Hoskins ◽

V. Williams ◽

V. Allison

Keyword(s):

Diffraction Grating ◽

The Other ◽

Carbon Replica ◽

Electron Microscopes ◽

The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

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