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Normalization can also more broadly refer to when a voter's rated ballot is adjusted to fit between any two scores i.e. if the highest score a voter gave anyone was a 3 out of 5, then in some situations, it is desirable to ensure that after normalization, the voter's highest score given to any candidate will still be a 3 out of 5. This can be the case when a voter does not want to use all of their voting power.
===Impossibility Theorems===
===Applicability of Arrow's theorem===
:''{{Main|Arrow's impossibility theorem}}''
[[Arrow's impossibility theorem]] demonstrates the impossibility of designing aan set[[Ordinal ofvoting]] rulessystem forwhich socialpasses decisiona makingset thatof woulddesirable obey every ‘reasonable’ criterion required by societycriteria. Some activists believe thatSince Arrow's theorem only applies to [[ordinal voting]] and not cardinal voting. They point out that that it is technically possible forsystems, several cardinal systems to pass all three fairnessthese criteria. The typical example is [[score voting]] but there are also several [[Multi-Member System |multi-winner systems]] which proport to pass all three of Arrow's original criteria. Additionally, there are cardinal systems which do not pass all criteria but this is not due to Arrow's theorem; for example [[Ebert's Method]] fails [[Monotonicity]]. Subsequent social choice theorists have expanded on Arrow's central insight, and applied his ideas to specific cardinal systems.
HoweverFurthermore, subsequentthere socialare choiceother theorists[[Voting haveparadox| expandedImpossibility onTheorems]] which are different than Arrow's centraland insight,apply andto appliedcardinal hissystems. ideasThe moremost broadly.relevant are Forthe example,[[Gibbard-Satterthwaite theorem]] and the [[Balinski–Young theorem]]. The [[Gibbard-Satterthwaite theorem]] (published in 1973) holds that any deterministic process of collective decision making with multiple options will have some level of [[strategic voting]]. As a result of this much of the work of social choice theorists is to find out what types of [[strategic voting]] a system is susceptible to and the level of susceptibility for each. For example [[Single Member system | Single Member systems]] are not susceptible to [[Free riding]]. The [[Balinski–Young theorem]] holds that a system cannot satisfy a [[Quota rule | Quota Rule]] while having both [[House monotonicity criterion | House monotonicity]] and [[Population monotonicity]]. This is important because quota rules are used in most definitions of [[Proportional representation]] and [[Population monotonicity]] is intimatly tied to the [[Participation criterion]].
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