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 ...

Before continuing on with the remaining details of this "River Rat" method I would like to point out rhree important features ... 1. In general under River, the closer to the leaves (i.e. the further upstream from the sroot node sink) the stronger the preferences, so the less likely those contests will fail ratification if tested, which makes the last resort NOTA option extremely unlikely. 2. The Ratification process is still both valid and free of temptation regardless of the provenance of the decision tree ... it could be constructed at random, so the method is robust with respect to the sincerity/insincerity of the strategic ballots that determine the precise tree structure. The ratification process is designed to correct insincerities as far as possible under the constraints that remove all incentives for manipulative contamination of the ratification ballots. 3. Under zero info conditions with rational voters, the root node will be ratified, and its value will be the sincere Condorcer Winner if there is one. NAIVE RIVER DRAUNAGE ---> BINARY TREE DRAINAGE If you look at the tributary structure of a drainage basin, from a distance it may appear that two tributaries enter a larger stream at precisely the same place, making it impossible to determine which tributary enters up stream from the other. But that is symmetry that cannot stably persist over time in nature ... a closer look will invariably reveal that one tributary slightly precedes the other, or that the two tributaries join each other slightly before their confluence joins the larger stream. Exceptions to natural symmetry breaking processes are a sure sign of intentional engineering, whether by muskrats, the Army Corp of Engineers, the Navy Seabees, Girl Scouts of the Beaver Patrol, or by intelligent life on Mars. So how do we disambiguate the River Method tributary structure? The basic rule is that the later tributaries to the same node should enter further downstream (i.e. closer to the root node) than the earlier tributaries. Suppose that two subtrees T1 and T2 are joined because the root node value of T2 is defeated by the value k of some node N of T1. Instead of just (irresponsibly) introducing a branch from node N to the root of T2, we introduce a new node N' between N and its parent node, and label this new node with its value k, the alternative that pairwise defeated the root value of T2. [If N had no parent, then this new node N' becomes the new root node of T1.] Building up the binary decision tree this way ensures that the earlier (more upstream) nodes are the ones whose values are less likely to fail ratification, since the River procedure locks in the strongest preferences first. So who would use this River Rat method? Any enlightened group that currently uses Ranked Pairs, MAM, CSSD or Split Cycle might enjoy trying it out. -Forest El lun., 14 de mar. de 2022 11:57 a. m., Forest Simmons < forest.simmons21@gmail.com> escribió: > 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 ... > > >