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Indifferent Sets

S. Figueira, J. S. Miller, A. Nies
2008 Journal of Logic and Computation  
For the class of Martin-Löf random sequences, we show that every random sequence has an infinite indifferent set and that there is no universal indifferent set.  ...  We prove the existence of co-c.e. indifferent sets, including a co-c.e. set that is indifferent for every 2-random sequence with respect to the class of random sequences.  ...  P-indifferent set.  ... 
doi:10.1093/logcom/exn101 fatcat:yxuksxvujrcmxd42wl4e4bpj2m

Smooth indifference sets

William S. Neilson
1991 Journal of Mathematical Economics  
Smoothness of indifference sets is proposed as a weaker notion of smoothness for preference orderings.  ...  The assumption of smooth indifference sets is consistent with smooth Hicksian demand functions but not smooth Marshallian demand functions.  ...  If the Gaussian curvature of an indifference set is zero at some point, then the indifference set is said to be flat at that point.  ... 
doi:10.1016/0304-4068(91)90008-h fatcat:u3xudw22lngunp7ymyzqixt274

Indifferent sets for genericity

Adam R. Day
2013 Journal of Symbolic Logic (JSL)  
Jockusch and Posner showed that there exist 1-generic sets that have indifferent sets [10]. Figueira, Miller and Nies have studied indifferent sets for randomness and other notions [7].  ...  Such an indifferent set can by computed by any set in which bounds the (weakly) 1-generic.  ...  1-generic set has as indifferent set which is GL 1 .  ... 
doi:10.2178/jsl.7801080 fatcat:mw4vtqrjevbtnlmqgeemhouqcu

Ranking Opportunity Sets, Indirect Utility and Indifferences

Tom Potoms, Luc Lauwers
2012 Social Science Research Network  
In case the preference relation on X is antisymmetric, then each indifference set is a singleton and this rule coincides with the indirect utility approach.  ...  The opportunity set with the highest number of maximal options represents the higher level of well-being. We label this rule as the indirect-utility-indifference rule.  ...  If two equally large opportunity sets select all options but one in the very same indifference class, then the opportunity sets are ranked according to the options outside this indifference class.  ... 
doi:10.2139/ssrn.2159172 fatcat:dyknqziqkbgzjmmdlabhva62oi

Notions of indifference for genericity: Union and subsequence sets [article]

Tejas Bhojraj
2021 arXiv   pre-print
Miller showed that there is no infinite universal indifferent set for 1-genericity.  ...  A set I is said to be a universal indifferent set for 1-genericity if for every 1-generic G and for all X ⊆ I, G Δ X is also 1-generic.  ...  We can similarly define a universal indifferent set for weak-1-genericity. Figueira, Miller and Nies coined the term 'indifferent' and examined indifferent sets for random sequences [3] .  ... 
arXiv:2104.13910v1 fatcat:lp3bd4yc3badtfp24j62bwmwg4

Incompatibility of Efficiency and Strategyproofness in the Random Assignment Setting with Indifferences [article]

Haris Aziz and Pang Luo and Christine Rizkallah
2016 arXiv   pre-print
It has been an open problem whether there exists a mechanism that satisfies the same properties when agents may have indifference among the objects.  ...  A fundamental resource allocation setting is the random assignment problem in which agents express preferences over objects that are then randomly allocated to the agents.  ...  For n = 3 and allowing for indifferences, the set of ex post efficient assignments coincides with the set of SD-efficient assignments. Proof.  ... 
arXiv:1604.07540v1 fatcat:korrgxpwifeshcotouhs3vdxoa

Coherent choice functions, desirability and indifference

Arthur Van Camp, Gert de Cooman, Enrique Miranda, Erik Quaeghebeur
2018 Fuzzy sets and systems (Print)  
We investigate how to model indifference with choice functions.  ...  Once this is in place, we present an axiomatisation of indifference in terms of desirability.  ...  Consider any coherent set of indifferent options I.  ... 
doi:10.1016/j.fss.2017.05.019 fatcat:jxdwdb34fjakvgvud2auyhjche

Incompatibility of efficiency and strategyproofness in the random assignment setting with indifferences

Haris Aziz, Pang Luo, Christine Rizkallah
2017 Economics Letters  
We will compactly represent a preference relation as a comma-separated list with all alternatives among which an agent is indifferent placed in a set.  ...  To show a statement for more agents, we add agents that are indifferent between all alternatives. Both constructions do not affect the set of efficient lotteries and incentives of agents.  ... 
doi:10.1016/j.econlet.2017.08.010 fatcat:nm5z4c56qbbe3aq7rso6bralga

Exponential utility indifference valuation in two Brownian settings with stochastic correlation

Christoph Frei, Martin Schweizer
2008 Advances in Applied Probability  
We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions.  ...  This yields an explicit formula for the indifference value b of B at any time, even with a fairly general stochastic correlation. Earlier results with constant correlation are recovered and extended.  ...  To the best of our knowledge, this is the first explicit result on exponential utility indifference valuation in a setting with nonconstant and nondeterministic correlation.  ... 
doi:10.1017/s0001867800002585 fatcat:fl42ml4zo5gitkfqsxjh6ue2cm

Exponential utility indifference valuation in two Brownian settings with stochastic correlation

Christoph Frei, Martin Schweizer
2008 Advances in Applied Probability  
We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions.  ...  This yields an explicit formula for the indifference value b of B at any time, even with a fairly general stochastic correlation. Earlier results with constant correlation are recovered and extended.  ...  To the best of our knowledge, this is the first explicit result on exponential utility indifference valuation in a setting with nonconstant and nondeterministic correlation.  ... 
doi:10.1239/aap/1214950210 fatcat:zole6uz4ujbmdfss6apqqgha3a

Indifference sets of reference points in multi-objective integer linear programming

Maria João Alves, João Clímaco
2001 Journal of Multi-Criteria Decision Analysis  
We investigate some properties of the reference points in MOILP and also the graphical representation of indifference sets for tri-objective problems.  ...  Since the non-dominated solutions are discrete in MOILP, there are multiple reference points that lead to the same solution, i.e. there are indifference sets on the reference point space.  ...  In this paper, we examine the indifference sets (regions) on the reference point space.  ... 
doi:10.1002/mcda.301 fatcat:iksc6y3mwzacti5gsnw4a55f2u

Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms

Jorge Alcalde-Unzu, Elena Molis
2011 Games and Economic Behavior  
In this paper, we propose a family of mechanisms, called Top Trading Absorbing Sets mechanisms, which generalizes the Top Trading Cycles to the general case in which individuals are allowed to report indifferences  ...  In the general case, in which indifferences are allowed, the strict core may be empty.  ...  Therefore, it is also necessary to propose a mechanism for the general case in which they can report these indifferences.  ... 
doi:10.1016/j.geb.2010.12.005 fatcat:ax2jffeinzgfxm6a3kjsccpcmq

Setting Thresholds to Define Indifferences and Preferences in PROMETHEE for Life Cycle Sustainability Assessment of European Hydrogen Production

Christina Wulf, Petra Zapp, Andrea Schreiber, Wilhelm Kuckshinrichs
2021 Sustainability  
Thus, thresholds are commonly used to prevent decisions based on results that are actually indifferent between the analyzed options.  ...  Indicators The LCSA indicator set comprises indicators from the LCA, LCC and S-LCA. The LCA is an established method to evaluate environmental impacts of technologies or products.  ...  They set a common 'difference threshold' equally for all analyzed indicators. Common thresholds include several aspects of uncertainty based on, e.g., inventory and impact assessment.  ... 
doi:10.3390/su13137009 fatcat:ipbjinwd2fdntbfodizzkg7j5q

Extend TOPSIS-Based Two-Sided Matching Decision in Incomplete Indifferent Order Relations Setting Considering Matching Aspirations

Bingwen Yu, Qi Yue
2017 Eurasia Journal of Mathematics, Science and Technology Education  
On this basis, the weighted satisfaction degree matrices are set up. The extended relative closeness matrices are determined by using an extended TOPSIS technique.  ...  This paper develops a method for two-sided matching decision in the environment of incomplete indifferent order relations.  ...  the matching matrix = [ ] × can be set up.  ... 
doi:10.12973/ejmste/78100 fatcat:uc7s6ih4a5fdjjtioo665i33wa

The uncovered set and indifference in spatial models: A fuzzy set approach [article]

John N. Mordeson, Terry D. Clark, Nicholas R. Miller, Peter C. Casey, Michael B. Gibilisco, Maryland Shared Open Access Repository
2021
In contrast to conventional approaches, fuzzy spatial models induce a substantial degree of individual and collective indifference over alternatives.  ...  Our definition results in an uncovered set that is, in most cases, contained within the Pareto set. We conclude by characterizing the exceptions.  ...  THE UNCOVERED SET AND INDIFFERENCE IN SPATIAL MODELS: A FUZZY SET APPROACH Cycling in Fuzzy Spatial Models In spite of substantial criticism [1] , a great number of spatial models are grounded in the  ... 
doi:10.13016/m2aiws-nlnj fatcat:g3shkeho7jckdk36sus4jv3i6a
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