| ▲ | dmurray 8 hours ago | |
I don't get this part > Here, you asked R0, R2 and R3 to abstain from casting further votes in the first three columns, signified by black x. If I can ask them to do that, and rely on them to go along with what I ask - why not skip all the middle steps and ask them all to vote for red? | ||
| ▲ | grogers an hour ago | parent [-] | |
In this incarnation, the only one who "wants" red to win is the first column. Every other column will choose whatever color it wants to win, subject to the rules of the game. It's a 2 step process: 1. Prepare - Collect a majority of rows such that each of them promises not to accept any color sent by columns to the left of the proposing column. Any colors which were already accepted are sent in reply, along with the column they were accepted in (if different colors were accepted, only the rightmost column for a given row matters). The color to be propagated by the proposer is that with the rightmost column number (or if none were accepted by that particular majority, anything may be selected) 2. Accept - for every row, set the color to the one chosen in step one for the proposing column, subject to the promises made in step 1. In this case, it's not shown well in the diagram, but by having a majority of rows promise for column 2, column 1 would already have a broken majority. Even if column 4 wanted red, since it received some already accepted colors, it has to choose from one of them based on the rightmost column (blue in this case) | ||