Parameterized Complexity Of Manipulation And Control In Judgment Aggregation For Uniform Premise-Based Quota Rules

The task of aggregating individual judgments on logically interrelated propositions is called judgment aggregation.The operation of judging the aggregation process was first studied by List and Dietrich et al.Endriss et al.studied and evaluated the aggregation process from the perspective of computation for the first time.Baumeister et al.extended their results on manipulation,introduced the concepts of bribery and control in judgment aggregation,and focused again on algorithm and complexity theory.In the control strategy scenario,that,the external manipulator attempts to affect the election result by adding or deleting the judge’s individual judgment set.Manipulation strategy scenario,means that,the external manipulator attempts to add a certain number of any type of individual judgment set with the purpose of making the final aggregated result closer to his expected result.Based on this,we use the preference types introduced by Dietrich and List to make a more regular comparison between the new aggregation results and the original aggregation results.Judgment aggregation is often vulnerable to various types of strategic scenarios.In the social choice theory and computational social choice,this thesis makes an in-depth study on the ways that affect the election results.In this thesis,the collective decision-making mechanism vulnerable to strategic behavior,whether from the agents participating in the operation,or from the external chairman or bribe operators,is not desirable,which will undermine our trust in them.The main purpose of this thesis is to accurately evaluate the vulnerability of collective judgment aggregation mechanism to these internal or external influences.we will employ NPhardness as such a complexity barrier to shield judgment aggregation against undesirable strategic behavior.Still,it should be the first step to study whether problems that formalize manipulative behavior can outright be solved in polynomial time or whether they are NP-hard,and this is what we do here for control in judgment aggregation.In this thesis,we study the manipulation problems in many cases from the perspective of computational complexity,provide effective algorithms for some judgment aggregation problems,and prove the stability of some aggregation rules.We expect to get their complexity results by studying the aggregation problems in the case of manipulation and control operations,and to provide some ideas and technical support for analyzing the complexity of aggregation problems.The main results are as follows:(1)for the control operation,the result manipulation is considered by adding,deleting and replacing the judge’s individual judgment set,and the computational complexity of the quota rule based on the unified premise under the preference type is studied.We obtain the result that the control operation problem is NP-hard.(2)In the control strategy scenario,for the behavior of adding,deleting and replacing personal judgment sets,considering the parameterized complexity under CR,HD and EXACT preference models,we conclude that the problem with the number of prerequisite items in the aggregation problem as the parameter is FPT,and the others are NP-hard and W[1]-hard.(3)In the manipulation operation,for the behavior that the chairman can add any type of individual judgment set,the parameterized complexity is analyzed.Three preference models are used to analyze,and the results of P and W[1]-hard are obtained.