• In this chapter, we examine whether the method by which democracies make choices has compelling qualities that make it morally or normatively acceptable in comparison to dictatorships, irrespective of any material gains.

• Arrow's theorem states that no technique of group decision-making can ensure a stable group decision while also meeting minimal fairness criteria. In fact, it demonstrates that there is no such thing as a flawless set of decision-making institutions; either fairness is compromised, or unstable group decisions are possible.

• The philosophy students among you could point out that we're missing some key criteria for evaluating sets of political institutions at this stage. For analyzing the moral or ethical worth of adopting a set of institutions, political philosophers often employ one of two main methods.

• People commonly believe that a dictatorial decision-making process is inherently unjust, whereas a democratic decision-making process is inherently just. In the sections that follow, we deconstruct this assumption and present a set of criteria for analyzing how groups of people make decisions.

• Many individuals claim they support democracy because they feel it is a fair method to make decisions as a community. The majority of group members' views should be reflected in collective decisions, according to one intuitive understanding of fairness.

11.1, Majority Rule and Condorcet's Paradox

• Increase (I), reduce (D), or maintain existing (C) levels of social service provision are the three alternatives offered. Assume the council consists of three members: a left-wing councillor, a right-wing councillor, and a centrist councillor, each of whom ranks the suggested choices differently.

• Let's pretend that the council makes decisions based on a majority vote. This means that any policy proposal that has the backing of two or more councillors will be accepted in this case.

• It's worth noting that no one option wins the majority of the time—each alternative only wins one pair-wise competition. This plethora of "winners" leaves the council with no clear policy direction. To put it another way, the council cannot decide whether to raise, decrease, or retain present levels of social service provision.

• This basic example yields a number of intriguing outcomes, which we will now investigate in further depth. The first is that a group (the council) made up of three rational actors (councillors) looks incapable of making a reasonable choice for the group as a whole.

• Each of the councillors in the case is rational since they have a full and transitive preference ordering over the three policy choices. The left-wing councillor, for example, favours I to C and C to D, as well as I to D.

• Condorcet's dilemma highlights the fact that individual rationality is insufficient to secure group rationality. A group of actors with complete and transitive preference orderings might act in ways that indicate group intransitivity. There is no such thing as a "majority" when this happens; instead, there is a cycle of various majorities.

11.1

• Imagine that preserving present social service spending is the status quo, and then consider who might gain from a change. Both the left and right-wing councillors want to suggest a change, according to the answer.

• However, if he suggested a reduction, both the centrist and left-wing councillors would vote against it. Similarly, the left-wing council member favours more social services over the existing quo. If he suggested an increase, however, both the centrist and right-wing councillors would vote no.

• The argument is that majority rule does not always have to conflict with reasonable group choices. Condorcet only demonstrated that it is conceivable for a group of people with transitive preferences to behave as though they have intransitive preferences. As a result, Condorcet's dilemma undermines our faith in majority rule's ability to create stable results only to the extent that we anticipate actors to have the preferences that lead to group intransitivity.

11.3

• As seen in Table 11.3, the city council scenario from which we started, in which a Condorcet winner fails to emerge from a contest among three choices and three votes, is a rare occurrence. Almost every logically feasible stringent preference ordering produces a Condorcet winner and, as a result, a stable outcome (94.4 percent).

• Consider what might happen if we added a little more realism to our hypothetical city council deliberating on social assistance spending. Previously, we reduced the problem to the councillors having to choose between three options: raise, decrease, or retain existing expenditure.

• To conclude, Condorcet's paradox shows that confining collective decision-making to a small number of rational people does not ensure that the group as a whole would behave rationally. When the range of viable options is small, group intransitivity is rare, but when the collection of feasible options grows big, it is nearly guaranteed that the majority rule applied to a pair-wise competition among alternatives will fail to provide a stable conclusion.

11.4, The Borda Count and the Reversal Paradox

• In 1770, Jean-Charles de Borda, a Condorcet compatriot, proposed the Borda count as an alternate decision-making procedure (published in 1781). 8 Individuals are asked to rank various options from most to least favoured, and then numbers are assigned to represent this rating.

• When we examine the inclusion of a hypothetical fourth option to the reference order we're looking at,10 a further problematic feature of this decision rule emerges.

• The right-wing councillor prefers it to all other choices except an immediate reduction, while the centrist councillor likes it to all other options save an increase. Table 11.5 summarizes the order of choice for each council member among the four possibilities.