In this post I discuss a proportional representation system called Interactive 
Representation (IR). A brief description of the system is followed by a 
discussion of some characteristics compared to traditional systems such as 
single-representative districts (the dominant paradigm in the United States) 
and proportional representation systems like STV.


OVERVIEW
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In traditional systems, a state is divided into e.g. 100 districts, and each 
district elects one representative to the legislature, where each 
representative gets one vote.

In IR, each district has multiple representatives. I believe that three or four 
would be a good number, but for simplicity I will assume two representatives 
per district for most of this post.

Voters are presented with ranked ballots. By a mechanism I will describe in an 
appendix, the winning candidates are selected. The highest-ranked winner on 
each ballot is the preferred winner on that ballot. Each representative casts a 
number of votes equal to the number of ballots on which he was the preferred 
winner.

A voter can leave candidates unranked; if no winning candidate appears on a 
ballot, then that ballot has no preferred winner. This is effectively the voter 
saying that he would rather be unrepresented in the legislature than be 
"represented" by someone who would vote contrary to his wishes.


CHARACTERISTICS
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PRECISION OF REPRESENTATION: EVERY VOTE COUNTS

In a single-winner district, your candidate may win or lose by, say, 5000 
votes. If you had not bothered to vote, the margin would have been 4999 or 
5001, and the end result would have been the same. Your one additional vote is 
effective discarded at the end of Election Day. This leads to a "My vote 
doesn't make a difference" mentality that discourages participation in the 
election. Even in STV, the proportion of elected representatives with a given 
political philosophy is a rounding of the proportion of votes cast for them.

In IR, by contrast, that additional vote sticks, and your chosen representative 
is one vote stronger in the legislature than he would have been without your 
vote. I believe this would encourage voter participation. Similarly, increased 
voter participation in your district means more representation for your 
district in the legislature, which I believe would also serve to encourage 
participation.


LOCALITY OF REPRESENTATION

In STV, it takes a large number of representatives to capture small changes in 
voter support. For example, it takes at least 12 representatives to reflect any 
differences between 45%, 50%, and 55% support. (Even at 12, those proportions 
get rounded to 5/12=42%, 6/12=50%, and 7/12=58%. A more precise reflection of 
voter support requires more representatives.)

In IR, those differences can be captured with as few as two representatives per 
district. This makes it feasible to have a large number of small districts. 
This has several advantages:

* It empowers the voter to select a candidate who reflects both his political 
philosophy and the interests of his particular district.

* It reduces the number of candidates and representatives with which the voter 
must be familiar in order to vote effectively.

* It makes each representative answerable to a relatively small constituency, 
which in turn gives each voter better access to his representative. By 
contrast, in STV each representative is answerable to a much larger 
constituency and each individual voter is therefore less significant. In 
single-winner districts, each representative answers to a small district, but 
those voters who are politically opposed to his positions have effectively no 
representative to go to.


IMMUNITY TO GERRYMANDERING

With single-winner districts, if Big-endians constitute 51% of the electorate 
in each of two districts and 0% of the electorate in a third, they elect two 
out of the three representatives from those three districts, and get two out of 
three votes in the legislature, despite constituting barely one third of the 
electorate.  With IR, they would get 34% of the legislative votes from those 
three districts, the same as their proportion in the electorate.

A similar feature is that representation automatically adjusts to reflect 
changes in the size of the electorate. Traditionally, districts are redrawn 
every so often in such a way that all districts have about the same population 
size. In between such redistrictings, population shifts can lead to some 
districts being overrepresented and others underrepresented. In IR, the 
redistricting process would be similar, but in between redistrictings, a 
population increase in a district would automatically mean a representation 
increase, assuming the additional population votes.


STABILITY OF LEGISLATURE MEMBERSHIP

I suspect opinions will be mixed on whether this is a good thing or a bad thing.

With single-winner districts, as the political views of the electorate 
vacillate between 51% Big-endian and 51% Little-endian, the Big-endian 
representative loses his seat to a Little-endian, who is then voted out of 
office in favor of a Big-endian, etc.

With IR, the Big-endian and Little-endian representatives would both be secure 
in their seats. As the politics of the district vacillates between 51% B and 
51% L, the voting strength of the two representatives changes, as 49% support 
is more than enough to maintain a representative's seat. The Big-endian 
representative will by voted out of office if support for Big-endianness drops 
to a very low level, or if Big-endian voters choose another Big-endian 
representative they like better.


NO PLACE FOR STRATEGIC VOTING (?)

STV is claimed to have little room for strategy, but there is certainly some. 
If a candidate needs 10,000 votes for election and your first choice receives 
15,000, then 2/3 of your vote counts for your first choice and 1/3 of your vote 
is transferred to your second choice. If you are confident that your first 
choice will be elected without your vote, it makes sense to demote him and 
transfer your entire vote to your second choice.

In IR, I can think of no realistic scenario in which insincere voting makes 
sense.


APPENDIX
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SELECTION OF WINNING CANDIDATES

Each voter ranks the candidates. From the ranking of candidates, we construct 
an implicit ranking of candidate sets, where the voter's preference between two 
candidate sets is defined as his preference between the most-preferred 
candidate in each set.

For example, let's suppose the district gets two representatives, and Joe Voter 
casts a ballot listing four candidates as such:

    A > B > C > D

Since there are two seats available, we look at candidate sets of order two. 
Joe's implicit ranking of the candidate sets is:

    {A,B}={A,C}={A,D} > {B,C}={B,D} > {C,D}

The Schulze Method is then applied to determine the winning candidate set. With 
modern technology, this is not difficult.
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