9814

Binary Election Sequences

This Demonstration shows how the sequencing of binary elections, in which voters choose between two alternatives, winnows multiple alternatives down to a single "winner." You can select (a) an electorate index that specifies the preferences amongst the magenta, blue, green and golden choices among all members of the electorate, (b) an election sequence index that specifies the sequence of choices faced by voters, and (c) the size of the electorate that will be permitted to vote. The Demonstration outputs rows showing, in the left column, the alternatives available in the election, and, in the right column, the electorate's preferences among the choices remaining after the loser from the binary election has been culled. The bottom right cell shows the choice that wins as a result of the election process.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Some political theorists have deprecated the capability of democracies by noting that control over the agenda and over the sequence of voting can lead to different electoral results. Arrow's impossibility theorem and considerable derivative work addresses this issue. This Demonstration helps see the circumstances under which these theoretical problems are likely to arise. As users will note, although it certainly does occur, it is somewhat unusual for the voting sequence to end up affecting the ultimate result.
Although the Demonstration shows only binary elections, the underlying code works on elections in which more choices are available and in which only the winning choice survives until the next round.
Sometimes, one or both of the choices in an election will no longer be available due to prior elimination. In that instance, the election is essentially "skipped" and the preference structure remains unchanged.
Snapshot 1: a golden result from one election sequence
Snapshot 2: a purple result from a different election sequence involving identical electorate preferences as Snapshot 1
Snapshot 3: an election sequence among a small electorate
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+