Ideal Representation

Ideal Representation is the property that the representation of the diversity of opinion of the population is exact and weighted by the relative importance to each voter. It is one of many types of representation which can be considered in a Representative democracy. It is expected to entail both partisan beliefs like those represented by Proportional Representation and regional desires like those represented by Proportionate Representation. It is not the state of everybody being totally represented but the state of optimal balance of representation. This balance extends beyond what is entailed in Balanced Representation. It is accepted that this is a theoretical tool used to think about the goal of an election method but not something which could ever be measured in practice. The reason for this is that there is no way to define and measure the true ideological space and everybodies position in it.

Lay people often mean Ideal Representation when they speak of Proportional Representation. The distinction is that Proportional Representation is only definable in terms of parties and individuals ideologies are rarely totally aligned with any party.

Introduction and Discussion
The biggest debate when designing a Representative Govenment  Electoral System is how to divide the electorate among the representatives and vice versa. This is a distinct choice prior to holding the election about which candidates a citizen could vote for and how that would translate into representation. Two logical requirements for this are that all citizens have a representative and all representatives have a similar number of citizens. These are the concepts of Petitioner Accountability and Balanced Representation, respectively.

The allocation of representatives to citizens is the primary issue of a representative democracy. For example, if the assembly contains 100 seats to fill, it still needs to be decided how citizens are to elect representatives for each seat. The historically most common and simplest way to do this is to have citizens grouped so that each group is entitled to elect who fills each seat. Forming each group at random from the population is clearly not useful, since the groups would be less prone to have a unique message for representation than other groupings. Since elections are in principle a delegative process, the primary split line between groups should be based on some feature of the citizens.

The ideal result of representation would represent all the political perspectives of all citizens weighted directly by the number who support each perspective. This Ideal Representation of the diversity of opinion is not possible. There are more mutually exclusive opinion groups than there are seats to be filled by representatives. Ideal Representation is the conception that this split is done so that the citizens are grouped optimally and each representative of each group optimally represents that group. Much of the debate surrounding electoral systems is rooted in the debate of how to best approximate ideal representation by splitting up the population into groups.

There are two well defined splits possible for systems, Partisan Systems and Regional Systems. In practical terms, this means voting for a person in Regional Systems or voting for a party in a Partisan System. These are closely related to the concepts of Proportionate Representation and Proportional Representation which define the typical outcomes of such systems. The degree of Proportionate Representation for each region is defined by the difference between the percent of seats obtained and the percent of the population (not voters) in that region. The degree of Proportional Representation for each party is defined by the difference between the percent of seats obtained and the percent of the popular vote for that party. If one wants to combine each of these differences into a global measure there are many methods to accomplish this. The typical measure for Proportional Representation is the Gallagher index.

Regional Systems tend to have a high degree of Proportionate Representation and Partisan Systems tend to have a high degree of Proportional Representation. It is important to clearly distinguish between the design structure of a system and the expected outcome for each type of representation. All systems either have some amount of Proportional Representation although it may not be able to be defined adequately. Proportionate Representation is more difficult because in systems where there are no defined regions no useful statement can be made. However, many systems commonly have outcomes where some regions or parties elect no representatives even though they have the population to warrant representation.

In Regional Systems, such as the standard Westminster System, the division is done by regional boundaries to form constituencies of equal population. The elected member is to represent all people in a regional constituency, not just those who voted for them. This means that every citizen is represented by one member of the assembly and each member represents a similar number of citizens. This implies that members are expected to represent citizens who did not vote for that member or did not vote at all. In Partisan Systems, the division is along partisan lines and citizens vote for parties not candidates. Each member is to represent the people who share the values of the political party the representative is a member of.

Despite the apparent symmetry between Regional and Partisan systems it is better to think of them as opposites in a number of ways. A country can be divided into constituencies of equivalent population with relative ease to guarantee Proportionate Representation at the finest grain. However, the space of political opinions cannot be divided in such a manner so political parties are used as a grouping for Proportional Representation. In most Regional Systems, there are an equal number of seats per region by design but in Partisan Systems the number of seats per party is determined by the election itself. Parties overlap in the opinion space and there are often minority views which do not have the power to start a party. This means, the delegation process is less clear in Partisan Systems as not all citizens have a political stance represented by an elected party so not all citizens have a representative. Since this tends to affect minority groups more often Partisan Systems then to result in a lack of representation for individuals who already do not have much political power. On the other hand, citizens who are adherents of a political party can have many associated representatives organized by the party. They gain political power through this organization. Furthermore, it is unclear in such systems if all members represent the same number of citizens and Balanced Representation is fulfilled. A citizen may have regional interests outside of the region they happen to reside in. A citizen with a particular ideological position is very unlikely to advocate for other ideological positions.

Definition
There is no clear definition of Ideal Representation because it is thought of as being idealized. It is expected to optimally represent both the ideological and regional considerations. In both Regional and Partisan Systems, it is possible that there are citizens with concerns that are not represented appropriately. Therefore, neither Regional nor Partisan Systems are what is desired from the theoretical standpoint of wanting to fulfill Ideal Representation. Due to the number of possible views in the intersection of the number of possible issues it is clearly impossible to represent each citizen’s nuanced political belief structure in a balanced manner. This is due to the associated problem of how each issue should be weighted against each other. What value is desired to optimize on? Most freedom? Least suffering? Most opportunities? Least coercion? Equality of treatment? Equality of outcome? In a broad sense, a system can only optimize for one value, so to attempt a system which represents issues in a combined way is impossible. This is the core motivation for representation of the people themselves not the people’s issues directly. It is understood that this abstraction loses some theoretical utility but it must be done since the utility is unquantifiable. This unquantifiability is the same issue as the imprecise definition of “best” way for the member to represent their citizens.

The cleanest definition is arrived at through a though experiment. Imagine every issue that any member of parliament could act upon is represented in a high dimensional space with each issue being one dimentsion. These issues could be regional, ideological, theological, ect. Each dimension has a number of opinions which each citizen could have. This means that each citizen could be represented as a single position in this "Opinion Space". Under this conception an even down sampling of the population in this space would result in the best possible Ideal Representation. This means that a Sortition would yield the highest Ideal representation.

While the sortition is useful for the though experiment there are a number of issues. The most glaring is that a random sampling would not select quality candidates but average candidates. One wants an election system which selects the average person in the Opinion Space but the best the country has to offer in terms of credentials and virtue. While many criticize that the quality of politicians is low few would dispute that the average politician is better at being a politician than the average citizen. The more complex issue with defining a sortition as the best system based on Ideal Representation is that this "Opinion Space" is only hypothetical. In fact, this space could be different for each person in a way that makes combining them impossible.

Another way to view this problem is in terms of Cross-cutting cleavage. If the fraction of representatives on either side of all possible cleavages matches the fraction of citizens then Ideal Representation has been achieved. Clearly rounding issues come into play here but if you average across the infinite number of cleavages then you get an exact number in theory.

Further Explanation

 * Yale lecture on the Cross-cutting cleavage