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Topic: Independence of irrelevant alternatives

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Voting system

Sidney Morgenbesser

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	Independence of irrelevant alternatives - Wikipedia, the free encyclopedia
		Independence of irrelevant alternatives (IIA) is an axiom often adopted by social scientists as a basic condition of rationality.
		The independence of irrelevant alternatives is an assumption of the multinomial logit model in econometrics; outcomes that could theoretically violate IIA (such as the outcome of multicandidate elections, or per Arrow any choice made by humans) may make multinomial logit an invalid estimator.
		As an alternative, the conditional logit model may be used if the structure of decision-making can be reduced to a series of binary choices; this approach also avoids the IIA assumption.
	en.wikipedia.org /wiki/Independence_of_irrelevant_alternatives (827 words)

	Strategic nomination - Wikipedia, the free encyclopedia
		If these are the only cases in which a change in the candidate set leads to a different election outcome, then the voting system is independent of irrelevant alternatives and therefore immune to strategic nomination.
		Independence of irrelevant alternatives, however, is a very hard property for a voting system to satisfy.
		Independence of clones was first formulated by Nicolaus Tideman in his article, Independence of clones as a criterion for voting rules.
	en.wikipedia.org /wiki/Strategic_nomination (731 words)

	Arrow's impossibility theorem - Wikipedia, the free encyclopedia
		Arrow was a co-recipient of the 1972 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel (popularly known as the “Nobel Prize in Economics”).
		independence of irrelevant alternatives: if we restrict attention to a subset of options and apply the social welfare function only to those, then the result should be compatible with the outcome for the whole set of options.
		Indeed, the IIA criterion is the one breached in most useful voting systems.
	en.wikipedia.org /wiki/Arrow%27s_Impossibility_Theorem (1992 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		IIA does not distinguish between alternatives that are not even included in the set of available alternatives, and alternatives that belong to that set but are not now under explicit consideration.
		The alternatives have to be evaluated because it is not possible to study the welfare consequences of strategic voting by imposing conditions on the \emph{voting rule}.
		IIA, in turn, cannot be used to evaluate the alternatives directly, because it is a condition on the social welfare function(al).
	www.valt.helsinki.fi /staff/alehtine/cwnorm.rap (5342 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		^iia^ can also be used in more general contexts where the conditional maximum-likelihood estimator for the logistic regression model is applicable, e.g., in fixed-logit models where the different responses within groups are substantively linked between groups via the ^code^ variable.
		^iia, code(means)^ Some fun ("Substantive background") ----------------------------------- IIA is the notorious assumption in individual decision theories and in social choice theory that the choice (preference) between a collection of alternatives is not affected if non-chosen alternatives are made unavailable.
		Under IIA, b(restricted) and b(overall) should be approximately equal, while IIA is violated if the two estimates of b are different.
	www.fss.uu.nl /soc/iscore/stata/iia.hlp (637 words)

	Quantitative Methods in Public Administration
		Independence from irrelevant alternatives: The order of preferences among the given alternatives in the vote is not affected by alternatives not being voted on.
		Consider three alternatives, A, B, and C. Let Voter 1 prefer A to B to C. Let voter 2 prefer C to A to B. Let Voter 3 prefer B to C to A. If there is a vote on A and B, A wins.
		That is, majority voting leads to a topical (transitive) preference ordering among alternatives if the number of choices is odd and preferences are single-peaked (there is only one criterion or dimension for ranking) and in one direction (all voters rank the same from low to high, agreeing on what is "low").
	www2.chass.ncsu.edu /garson/pa765/socialchoice.htm (924 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		If any alternative occurs at the top of at least half the preference lists, then it is declared to be the social choice (or at least tied for such), and the process is completed.
		If no alternative is on top of half of the lists, then we delete the alternative(s) that is at the bottom of the most lists.
		Each person chooses a set of alternatives (presumably the top k alternatives on his or her preference list, where the person decides what k should be).
	www.goshen.edu /~dhousman/math100/Handouts/Day09.doc (552 words)

	[No title]
		When alternatives are independent, the decision-makers’ choice does not depend on the presence or absence of other alternatives in the choice set.
		The set of alternatives to the incumbent party affects whether there is an alternative governing coalition, a depository of protest votes, or no way for a voter to register her displeasure.
		These equations allow for the possibility that the choice process is not neutral with respect to the decision and allows independence of irrelevant alternatives to be violated with the size of the choice set changes. These models are consistent with Sen's (1997) arguments that preferences may be sensitive to the choice process.
	www.duke.edu /~rml5/dis/PoliTheory1.doc (7924 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		A voting system satisfies independence of irrelevant alternatives if it is impossible for an alternative B to move from nonwinner status to winner status unless at least one voter reverses the order in which he or she had B and the winning alternative ranked.
		If two or more alternatives remain and all of theses remaining alternatives would be eliminated in the next round, then these alternatives are declared to be tied for the win.
		Monotonicity- if an alternative is a winner, and a new election is held in which the only ballot change made is for some voter to move the former winning alternative higher on his or her preference list, then the original winner should remain a winner.
	www.svsu.edu /~agm/m125-Ch12-NOTES-w05.htm (608 words)

	Multinomial Discrete Choice Modeling
		See the section "Independence from Irrelevant Alternatives (IIA)." The nested logit model is derived by allowing the random components to be identical but nonindependent.
		Instead of independent type I extreme value errors, the errors are assumed to have a generalized extreme value distribution.
		Individual i chooses alternative j if and only if it provides a level of utility that is greater than or equal to that of any other alternative in his choice set.
	support.sas.com /91doc/getDoc/etsug.hlp/mdc_sect21.htm (452 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		Independence of Irrelevant Alternatives Criterion: If a candidate wins an election, then that candidate should also win a re-election with one of the other (irrelevant since they did not win) alternatives (candidates) removed.
		It is possible for the winner of an election to lose in a re-election with one of the losing candidates removed when the Borda count method is used.
		This is what we mean when we say the Borda count method violates the independence of irrelevant alternatives criterion.
	www.sju.edu /~amyers/TEACHING/1171/SVMotivate.ppt (428 words)

	Voting (Site not responding. Last check: 2007-10-14)
		In class, I said that the independence of irrelevant alternatives was a very strong assumption.
		In summary, one reason that the independence of irrelevant alternatives is a questionable assumption is that it does not allow a social choice mechanism to unambiguously guess preference strengths from preference orderings, and then use these preference strengths to generate a societal preference ordering.
		Thus, the electoral college is not independent of irrelevant alternatives.
	students.cs.byu.edu /~cs670ta/Lectures/Voting.html (1713 words)

	Arrow's Theorem (Site not responding. Last check: 2007-10-14)
		Our monotonicity criterion and criterion of independence of irrelevant alternatives are simplifications of his.
		Thus a democratic society must choose between a non-universal procedure (only certain kinds of preference ballots may be cast) or a procedure that violates independence of irrelevant alternatives (fringe candidates may affect outcomes of elections).
		Then the plurality method is used and we know this can violate the criterion of independence of irrelevant alternatives.
	www66.homepage.villanova.edu /thomas.bartlow/mat1220/handouts/arrowthm.htm (451 words)

	Economics and Economic Justice
		When there is sufficient homogeneity among preferences, for instance when alternatives differ only in one dimension and individual preferences are based on the distance of alternatives to their preferred alternative along this dimension (think, for instance, of political options on the left-right spectrum), then consistent methods exist (the majority rule, in this example; Black 1958).
		His solution consists in choosing the alternative which, in the feasible set, maximizes the product of individual utility gains from the disagreement point (this point is the fallback option when the parties fail to reach an agreement).
		Egalitarian-equivalence is a serious alternative to no-envy for the definition of equality of resources, and its superiority in terms of solidarity is quite significant, in relation to the next point.
	plato.stanford.edu /entries/economic-justice (11443 words)

	[No title]
		The utility that an individual associates with an alternative is specified to be the sum of a deterministic component (that depends on observed attributes of the alternative and the individual) and a random component (that represents the effects of unobserved attributes of the individual and unobserved characteristics of the alternative).
		However, it is saddled with the “independence of irrelevant alternatives” (IIA) property at the individual level (Ben-Akiva & Lerman, 1985); that is, the multinomial logit model imposes the restriction of equal cross-elasticities due to a change in an attribute affecting only the utility of an alternative i for all alternatives EMBED Equation.3 .
		The IIA assumption holds only if the scale parameters of all the alternatives are equal, in which case the heteroscedastic model collapses to the multinomial logit model.
	www.ce.utexas.edu /prof/bhat/ABSTRACTS/CITYNEW2.doc (5202 words)

	Independence of irrelevant alternatives at opensource encyclopedia (Site not responding. Last check: 2007-10-14)
		In voting systems, independence of irrelevant alternatives is the property some voting systems have that, if one option (X) wins the election, and a new alternative (Y) is added, only X or Y will win the election.
		A less strict property is sometimes called local independence of irrelevant alternatives.
		It says that if one option (X) wins an election, and a new alternative (Y) is added, X will win the election if Y is not in the Smith set.
	www.wiki.tatet.com /Independence_of_irrelevant_alternatives.html (214 words)

	[No title]
		The "ordinal" rankings violate independence of irrelevant alternatives (see below), which is a prohibition against the use of cardinal information in schemes like this.
		If F satisfies Unanimity and Independence, then there exists an ultrafilter on I such that for all profiles and and all x and y: if the set of individuals that prefers x to y belongs to the ultrafilter, then x is preferred to y by society.
		Given a set A of alternatives and a set N of people, each of whom has a complete, transitive, etc. preference ordering Ri on A, we seek a social preference ordering R on A. R must also be complete and transitive.
	www.sdc.org /~ksjim/arrow.txt (2319 words)

	A characterization of the Nash bargaining solution
		While three of Nash's axioms are quite uncontroversial, the fourth one (known as independence of irrelevant alternatives) raised some criticisms, which lead to two different lines of research.
		The first three papers replace IIA by several axioms together with some kind of continuity, the next two replace IIA and other axioms by one axiom, and lastly Lensberg (1988) replaces IIA with consistency, therefore a domain with a variable number of agents is needed.
		In this paper we provide an alternative characterization of the Nash bargaining solution in which the axiom of independence of irrelevant alternatives is replaced by three different axioms.
	www.nirdagan.com /research/200003 (584 words)

	Ethnographic Decision Modeling (Site not responding. Last check: 2007-10-14)
		Part of the conception is that there is a set of somehow comparable alternatives among which to choose.
		Each alternative is a bundle of features or aspects, just as we have been assuming in cultural domain analysis.
		For example, in micro-economic models, a key axiom is IIA ("independence of irrelevant alternatives") which begs the question of what is relevant and what is not.
	www.analytictech.com /mb870/Handouts/ethnographic_decision_modeling.htm (166 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		Yet it is widely known that a potentially important drawback of the multinomial logit model is the independence from irrelevant alternatives property.
		While most analysts recognize the implications of the independence of irrelevant alternatives property, it has remained basically a maintained assumption in applications.
		The basic idea for the test here is to test the reverse implication of the independence from irrelevant alternatives property.
	emlab.berkeley.edu /pub/wp/mcfadden_abs/4.11 (251 words)

	Voting (Site not responding. Last check: 2007-10-14)
		The definition of irrelevant does not mean unimportant; rather, it means that the option is irrelevant in determining the preferences among the other options.
		Although the data is only approximate and should not be blindly accepted, this example demonstrates that the plurality voting protocol is not independent of irrelevant alternatives.
		In the electoral college voting mechanism used in the Unites States, citizens vote within their states for a presidential candidate and the winner of that state carries that state's electoral votes.
	students.cs.byu.edu /~cs670ta/MechanismDesignNVoting.html (2614 words)

	Michael Nielsen » Blog Archive » Limits to collective decision making: Arrow’s theorem
		However, for the purposes of this discussion we’re going to assume that this property of respecting the independece of irrelevant alternatives is regarded as highly desirable.
		Stated another way, what Arrow’s theorem shows is that the requirements of respecting unanimity and the independence of irrelevant alternatives are incompatible with a third desirable requirement, namely that the voting system not be a dictatorship.
		It follows from the independence of irrelevant alternatives that the overall ranking of
	www.qinfo.org /people/nielsen/blog/?p=254 (2336 words)

	Condorect sub-cycle rule
		Definition ("Modified Independence from Irrelevant Alternatives Criterion"): A method meets the "Modified Independence from Irrelevant Alternatives Criterion" (MIIAC) if and only if: An additional candidate, who is not in the Smith set, cannot change the result of the elections.
		Definition ("Generalized Independence from Twins Criterion"): A voting method meets the "Generalized Independence from Twins Criterion" (GITC) if and only if additional twins cannot change the result of the elections.
		That means, that the optimal strategy for the voters is independent from whether the voters vote for or against candidates.
	lists.electorama.com /pipermail/election-methods-electorama.com/1997-October/001544.html (3381 words)

	st: Re: Hausman test for Independence from irrelevant alternatives
		I want to run a conditional logit and I > have 3 alternatives such as C:keeping current policy (baseline group), > A:protection policy (1), B:protection policy (2).
		Description ----------- iia performs specifications tests for clogit and mlogit, namely Hausman tests for the assumption of "independence of irrelevant alternatives" (IIA) for each of the alternatives.
		Previous by thread: st: Hausman test for Independence from irrelevant alternatives
	www.stata.com /statalist/archive/2003-04/msg00710.html (244 words)

	The Solution to Arrow’s Difficulty
		It is shown too that Arrow’s axiom of the Independence of Irrelevant Alternatives is not realistic, and thus unattractive.
		Alternatively put, the new result in this paper comes from widening the scopes of utility and rationality to the inclusion of the constitutional process itself.
		Alternatively, if the idea is that these axioms concern educated people, then there is a hidden inconsistency, in that reasonable agents are assumed to regard inconsistent axioms as reasonable.
	www.dataweb.nl /~cool/Papers/SocialWelfare/Arrow97c.html (5206 words)

	Tutorial Exercises I (Site not responding. Last check: 2007-10-14)
		Suppose there are two individuals, 1 and 2, and three alternatives, x, y, and z.
		Social preferences are then determined by adding up points for each alternative.
		(a) Construct an example such that independence of irrelevant alternatives is violated.
	www.st-andrews.ac.uk /~jpt/teaching/ex3.htm (328 words)

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