[EM] River Ratification

[Forest Simmons]

The idea of using a second ballot for sincere ratification can be applied
to elections having a binary decision tree structure.

And the customary non-binary tree  tributary system or drainage basin
structure of Heitzig's River method can be "lifted" to a decision tree form
appropriate for the sincere ratification process.

Before delving into the details of the tree construction, let's see by
example how such a tree might enable a sincere ratification process:

Let's represent our decision tree example in nested set form:
{{A p B} q {C r D}} s {{E t F} u {G v H}},
where the upper case letters represent alternatives, while the lower case
letters represent nodes.

Eventually each node will have a "value", namely the pairwise winner of the
recursive values of the root nodes of its two branches.

Suppose, for example that letters nearer the front of the alphabet are
preferred pairwise over later letters, then the node values could be
displayed thusly:

{{A A B} A {C C D}} A {{E E F} E {G G H}}.

The final decision A is the value of the root node.

For ratification we use the (sincere) ratification ballots to test if A
truly is the sincere preference in the pairwise contest A vs E.

If so, then A's win is certified as ratified, binding, and dispositively
irrevocable ... end of story.

If not, then the same sincere ballot set is used to test E's putative
pairwise victory over G.

If that victory is confirmed, then E is certified as the election winner
... end of story.

If not, then the same ratification ballot set is employed to test the
supposed pairwise preference of G over H.

If G's defeat of H is confirmed, then G's victory is taken to be duly
ratified, and G is dispositively elected.

Otherwise, H wins by default, unless H is the Condorcet Loser on the
sincere ballots, in which case NOTA wins, and the election must be scrapped
and started over from scratch.

To be continued ...
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