What is the borda ranking and who is the borda winner

Assignment Help Basic Statistics

Reference no: EM131333661

The Borda and Condorcet Methods:- The following example was presented by Condorcet, in a critique of the Borda Method. A committee composed of 81 members is to choose a winner from among three candidates, A, B, and C. The rankings of the committee members appear in the following table:

No of voters	First Candidate	Second Candidate	Third Candidate
30	A	B	C
1	A	C	B
29	B	A	C
10	B	C	A
10	C	A	B
1	C	B	A

(a) Is there a Condorcet winner? If yes, who is the Condorcet winner?

(b) What is the Borda ranking, and who is the Borda winner?

A counterclaim to Condorcet's critique might be given by analyzing the preference profile in the following way. A Condorcet component is a set of 3n individuals whose strict preference relations are as follows:

No of voters	First Candidate	Second Candidate	Third Candidate
ⁿ	^a1	^a2	^a3
ⁿ	^a3	^a1	^a2
ⁿ	^a2	^a3	^a1

The variables a₁, a₂, a₃ are three distinct alternatives (this example can be generalized to an arbitrary number of alternatives). In a certain sense, these voters "neutralize" each other, and they can therefore be removed from the list of voters.

(a) What are all the Condorcet components in this example?

(b) Remove all the individuals appearing in one of the Condorcet components. From among the remaining individuals, find another Condorcet component and remove all the individuals in that component. Repeat this process until there remain no Condorcet components. Is there a Condorcet winner according to the strict preference profile that remains at the end of this process? If so, which candidate is the Condorcet winner?

Reference no: EM131333661

Questions Cloud

Explain the different strategies for growth : Explain the different 'strategies' for growth employed by deciduous and coniferous trees in mid-latitude areas and relate these differences to climatic conditions. In your answer, explain the difference between deciduous and coniferous trees.

Performs insertions and deletions on a doubly linked list : In a doubly linked list each node has two pointers (except at the head and tail), one to its successor and one to its predecessor. (This allows for list traversal in both backward and forward directions.)

Design algorithms that search and maintain such linked list : Under this scheme the most frequently retrieved items eventually migrate to the front of the list. Design algorithms that search and maintain such a linked list.

Discuss ken liability to len if any for any intentional tort : Ken hates Len. One day Ken sees Len riding his horse on the Bridle Path. Ken runs up to Len and kicks Lens horse in the leg. Discuss Ken's liability to Len, if any, for any intentional torts

What is the borda ranking and who is the borda winner : Is there a Condorcet winner? If yes, who is the Condorcet winner?- What is the Borda ranking, and who is the Borda winner?

Design and implement list insertion and deletion algorithms : That is, all unused storage should be linked together in a list. When a new item is deleted it is placed on the end of the free list and when a new item is inserted the space should be taken from the end of the free list.

Foreign exchange currency risk with its forward market hedge : Suppose a U.S. firm buys $300,000 worth of textiles from a Peruvian manufacturer for delivery in 60 days with payment to be made in 90 days (30 days after the goods are received). The rising U.S. deficit has caused the dollar to depreciate against th..

What approach to ethical decision making does jeremy use : Jeremy's ethical decision making is guided primarily by his belief that his self-interests should be promoted as long as he doesn't harm others. What approach to ethical decision making does Jeremy use

Analyze conceptual framework with reference to annual report : Analyze the conceptual framework with reference to the annual reports of your chosen companies in light of the reporting requirements imposed on accountants and those charged with governance of corporations.

User Account

All Pages