VoteFair  ranking

Voting ID:

About VoteFair ranking

VoteFair Marble Machine

Watch marbles do Condorcet-Kemeny-VoteFair voting calculations

This marble machine does VoteFair popularity ranking (which is mathematically equivalent to Condorcet-Kemeny calculations) for three choices.

Below is a rough sketch of the VoteFair marble machine, an explanation for how it works, and instructions for building one.

VoteFair marble machine sketch

How it works

One set of "voting" marbles — preferably of a larger size — are used for the voting.  A voter would deposit their first voting marble into the opening that is marked with their first choice.  When marbles stop moving, the voter would deposit their second voting marble into the opening marked with their second choice.

Another set of "tally" marbles — preferably of normal size — would be the ones that are controlled by the voting marbles.  There would be nine tally marbles that would have to be deposited prior to each voter putting in their voting marbles.  The upper-right part of the machine uses "alternating" rockers and a "one-time-only" rocker to distribute those nine tally marbles onto nine "choice-dependent" rockers, where they would wait until the voting marbles are deposited.

A voting marble, as it drops down one of the 3 voting columns (on the left) would hit levers that are connected to the "choice-dependent" rockers.  Each lever is connected to three such rockers.  This action chooses whether a tally marble — on a "choice-dependent" rocker — goes left or right into a channel that directs the tally marble into one of six "result" columns (at the bottom right).

At the end of the voting, visually identify which result column has the most tally marbles.  That result column would have a label that indicates which is the first/winning choice, which is the second choice, and which is the third (least-popular) choice.

The machine also does plurality counting, which allows for comparison using traditional (simplistic) counting.  This counting is done using the larger "voting" marbles.  A voter's first marble goes into a "plurality-results" area (in the lower left) that is associated with the voter's first choice.  The voting marbles for secondary choices are sent to a "wasted secondary preferences" bin.

Suggestions for building

Here are suggested instructions for building the VoteFair marble machine. These instructions are being written without having actually built the marble machine, so do not blindly follow these suggestions in situations where something else makes more sense.

  1. Design, make, and test the "alternating" rockers that simply alternate which of two paths is taken by each successive tally marble.  Each such rocker tilts the opposite direction when a marble drops onto it.  The (optionally) pointed top part of the rocker simply moves left and right so that the next marble hits the opposite side of that pointed part.  The horizontal part of the rocker uses the weight of the marble to tilt the rocker to the opposite position.  (There are YouTube videos showing different designs for this kind of rocker.)  Seven such rockers are needed.  (They do not need to be reset.)
  2. Design, make, and test four "one-time-only" rockers.  Basically they are like an alternating rocker with one side of the horizontal portion missing.  One such rocker directs the first tally marble into one direction and then directs all the remaining tally marbles to go the opposite direction.  Three other such rockers direct secondary voting marbles into the plurality-area's "wasted-secondary-preferences" bin.  (For an advanced design these rockers would be reset automatically after a voter has voted.)
  3. Design, make, and test the "choice-dependent" rocker mechanisms.  A tally marble comes from the top, is slowed down by a two-dimensional funnel-like shape, and drops into an indentation on this rocker.  Then a small rotation of this rocker tilts the marble off the indentation and drops it to the left or right.  Nine of these mechanisms are needed.
  4. Design, make, and test the "vote-trigger" levers that control the choice-dependent rocker mechanisms. These are the levers that the voting marbles hit.   Each such lever should reset itself (using gravity) after a voting marble has hit it.  Six such levers are needed (two for each choice).  These should be designed in conjunction with the next step.
  5. Design, make, and test the connection between each vote-trigger lever and it's three associated choice-dependent rockers.  This connection can use two strings, or two wires, or one or two thin dowels.  If strings or wires are used, one string or wire must attach above the rocker's pivot point (connecting it to similar points on the connected rockers and a location above the pivot point of the vote-trigger lever) and a separate string or wire must attach below the rocker's pivot point (connecting it to similar points on the connected rockers and the downward-pointing lever of the vote-trigger lever).
  6. Mount a large rectangular (wooden) board in a way that keeps it inclined at a 45 degree angle, oriented so that it is taller than wide.  The incline causes the marbles to roll instead of drop, which slows them, to make them easier to watch.  If the voting marbles need to have more force for hitting the levers, the board can be inclined to be somewhat more vertical.
  7. Figure out the needed locations for everything, including the various rockers and the (wooden) barriers that will form channels and ledges along which the marbles roll.  Make sure the voting marbles and tally marbles go where they are supposed to go according to the above sketch, keeping in mind that this sketch is not a blueprint and does not show actual locations, just general paths.  If the marbles that cross paths are not correctly crossing paths, bridges can be built, and if easy-to-build bridges are desired, they can be made from plastic tubing that is split lengthwise.  There needs to be a time delay between when a voting marble hits its first lever and when it hits the second lever in the same channel (so that the first-released tally marbles have time to get out of the way of the second-released tally marbles), so there should be a funnel-like shape between the successive levers (which forces the marble to bounce before it reaches the opening).
  8. After working out the paths, fasten the rockers to the main board, and glue (wooden) barriers to the large board to form the channels and ledges (and bridges if needed).
  9. Try it out!  Invite friends/classmates to use it to rank three choices (such as favorite ice-cream flavor).  Refine it as needed.
  10. Finally, create a video of it, and post it on YouTube!  Then, send the URL to this website so that a link to your video can be added to this page.
  11. Appreciate that you are helping to teach how voting should be done, namely by using "pairwise" counting — instead of trying to use simplistic two-choice counting for more than two choices.

(Another possible enhancement is to add a crank or electric motor that feeds the nine tally marbles into the machine one at a time.  The crank approach can use a disk that has nine holes (or indentations) that each fit one marble, and the holes can pass by a tube stacked with marbles and then, a moment later, pass by an opening that allows the captured marble to exit from the disk.  If an electric motor is used, it can power an oscillating (back-and-forth-moving) block that has a hole that fits one marble, and that hole can move between a stack of marbles and an opening through which the captured marble drops.)


© Copyright 2011 by Richard Fobes, the author of The Creative Problem Solver's Toolbox and the inventor of VoteFair ranking as described at  You have permission to use these plans to create this marble machine if you include the word "VoteFair" in your machine's name, and your machine correctly calculates VoteFair ranking results.


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