Inndicidual To Docial Prefrences Flashcards
(43 cards)
What is the aggregation problem
The difficulty of combing individual preferences, behaviours, or constraints of multiple agents into a single coherent collective or social outcome e.g. the allocation of a public good or a political depiction, tax policy - as people value different thing s differently
What is the agency problem
Will the political process (voting) ensure that the desirable outcome of a ( canditate that actually represents the voters and follows through with their promises and act in the best interest of the voters) despite different goals ( asymmetric information, or weak accountability mechanisms)
Voters (principle) - delegating decision to the agent (political party / candidate)
What are institutions about other than laws
How collective choices are made and how collecting prefrences are aggregated - through democratic and consistent ways - aggregating individual prefrences and resolving conflicts
What is a stable match
A matching is stable if no two agents would each prefer prefers to match with each other over their over their partners e.g. roommate allocation / married couple)
There is no blocking pair
Example of a stable match
If their does not exist some pair kl such that either kl want to team up with either of in which makes both better off
Cheating example - if only one person wants to cheat then it still a stable match it but if both separate couples want to cheat then and prefer the other than it will be an unstable match
When does a stable match work
When it is not mutually profitable to break away from their partner and do better
What is a blocking pair
Where the deviations are mutually profitable and create instability
Two agents not matched to each other but who both prefer each other over their current match - indicating instability in their current match
Gale and shapely (1962)
Deferred acceptance algorithms ( men proposing to women example) ab xy
- multiple rounds and it ends when there are stable matches and no blocking pairs
two sided matching (men and women and school and student)
Irving (1985)
Efficient algorithm ( the stable roommate problem)
One sided matching - preference list and ranking
No blocking pairs (only stable matches)
You can either find a stable match or no stable match exists ( different from Gole and Shipley)
ABCD example D getting rejected
What are famous applications for the stable match problem
- hospitals and medical students
- students and schools
What did arrows impossibility theorm show
No desirable mechanism is able to aggregated individual prefrences consistently - political institutions cannot be neutral (aggregating individual prefrences are hard) Therfore it is impossible to design a fair voting system where everyone’s ranking options are made into a collective design - at least one desirable property is violated (otherwise it would be a dictatorship)
What does arrows impossibility therom believe
Dictatorship - any social welfare function which respects unrestricted domain, rationality, unanimity and independence of irrelevant alternatives
There is no ranked voting electoral system or social welfare function which allows
individual preferences to be aggregated in a consistent
way - unless the system is a dictatorship
No swf can meet all the five conditions when there are three or more policy options or at least two voters:
(i) unrestricted domain; (ii) rationality; (iii) unanimity; (iv)
independence of irrelevant alternatives (llA); and (v) non-
dictatorship.
Ruuin
What is the environment of the AIT
There is a finite set ( ABC） of at least three diffrent policy options
There a finite number of individuals i = 1,2…N
And each individual has a preference over the policy options
And you have to assume transitivity and completeness
Without transativity (preferences form cycles making désirions making to be impossible leading to contradictaty outcomes and makes finding the best option hard)
Without completeness: depiction making is impossible as agents cannot rank their preferences and things cannot be allocated Therfore all options need to be comparable)
Wha is social welfare function (SWF) / constitution
The mapping of individual preference relations into social preferences or preference aggregation rule - not a set of prefrences itself but a rule for generating a set of preferences for society
Goal: maximise utility of the country or maximise the utility of the worst off individual (Rawlism)
- evaluate policy / allocate resources/ framework for redistribution / equity vs efficiency
Wha is the objective of AIT
We are looking to aggregate prefrences - wanting to turn each possible set of individual preferences into prefrences relation <w for the society
What are the 4 properties of AIT
- social prefrences should repeat unrestricted domain (universality)
- Social preferences should respect rationality
- Social prefrences should respect unanimity
- The SWF should satisfy independence of irrelevant alternatives
Social prefrences should respect unrestricted domain (universality)
The social choice rule must work (defined ) for any set of prefrences over the alternatives ( dont rule put any preferences) - freedom of individual expression
Our SWF has to specify some set of social preferences <w for any given set of individual prefrences (>1, >2…>N)
Social prefrences should respect rationality
Social preferences should be complete and transitive like individual prefrences - otherwise their is no coherent choice rule
Social prefrences should respect unanimity ( Pareto optimality)
If everyone in society agrees that A is better than B the mapping should match that and SWF should define that social presence
The SWF should satisfy independence of irrelevant alternatives (IIA)
SWF should concentrate on the issues at stake, e.g. if society prefers A to B what people think of C shouldn’t matter
What does AIT prove if all 4 properties are respecte by SWF
A dictatorship - if the social prefrences always just reflets the same individuals prefrences e.g if there is an individual k that regardless of anyone’s prefrences picks A over B even if every o prefers B
What happens if we violate one of the 4 rules
- Unrestricted domain vio - where someindivisuals prefrences do not matter
- Violating rationality ( transitivity and completeness) condorcet pardox in parwise majority
- Vio unanimity - fixed social prefrences regardless of majority ( dictatorship)
- Vio IIA borda count
Individuals can lie about there preferences if they know that the result they actually want is off the table
Wha is the strongest restriction and why
IIA - we are ruling out anything cardinals about prefrences and simply focusing on prefrences being ordinal ( equal weighting of the cases at hand )
Furthermore there is no money to barter
However we ignore that AIT people may lie a pot their prefrences ( difficult to figure out people’s actual preferences) - as they may have incentive to lie to manipulate the outcome
What is a condorcet winner
When choosing policy for society we are looking for a clear cut winner - a policy that beats any other
feasible policy in a pair-wise vote.
Rank candidates - winner is the person ranked the highest - numbers are indicative of the posostion not the score
