President of the United StatesThe voters should cast Score  ballots based on the above range. The small count of possible values (4) makes hand counting practical.
Qualification of candidates to be on the ballot should not be based on parties and there is no need for partisan primaries and as I argue elsewhere, continuing partisan primaries harms democratic republicanism.
The electors that the State sends to the Electoral College must commit to score the candidates using the average of the scores determined by the citizen voters in their State.
In the electoral college, the winner should be determined by Score Voting. The range is on a scale of -50 to 50 with four significant digits of accuracy for the whole range. So for example -00.03 would be a valid score for an elector to assign to a candidate. So there are two significant digits in front of the decimal point and two more after it.
Single Winners Other than POTUSI'm proposing the following method for any US Senate seat when it comes up for re-election. I'm proposing this for any single-person office not involving an electoral college, such as State's Attorney General (Commonwealth's Attorney) or mayor of a city. I'm proposing this for the governor of a State unless the people can convert that office into a Swiss-style executive body.
Real and Virtual RunoffsState law should establish from time to time for these offices, a count of real runoffs and a count of virtual runoffs the public is willing to pay for. Payment includes not only money but also calendar time.
A real runoff entails the voters going to the official polling places and casting paper ballots.
A virtual runoff entails data being communicated from the precincts to a central tallying point. The election is only precinct-summable in case the count of virtual runoffs equals exactly zero. Tallying a round after the first requires knowing the global result from the prior round as to what candidates have been eliminated from the running.
Nonfinal PollingsWhen I say polling here, I'm talking about an instance where the public goes to the polling places and casts official ballots in an official election for public office. I don't know whether the term election should refer to each single polling or to the whole series of them used to elect someone to an office. But in either event, let me emphasize that I am not talking about opinion polling, but rather the exercise of power to put someone in office.
The count of nonfinal pollings is equal to the count of real runoffs. The sense of this is that the first polling is not a runoff and the rest of them are runoffs, and the final polling is final and the rest of them are not final. So you can see that each of these counts is the count of pollings minus one for filling a given office.
Each nonfinal polling should collect Score ballots using the range I give at the beginning of this writing. The round should eliminate candidates numbering approximately the ratio of the initial count of candidates to the count of real runoffs, but at least one. The remaining candidates are to be promoted to the subsequent round of polling. The ones promoted should be chosen by Reweighted Range Voting .
Final PollingThere are two cases.
Case of No Virtual RunoffsIf the decision prior to the election is to have no virtual runoffs, the final polling should collect Score ballots using the range I give at the top of this piece, and do an ordinary Score tally to determine the winner. 
Case of One or More Virtual Runoffs
Form of BallotIn this case each ballot consists of so many ranks as the voter chooses, where the order of the ranks on the ballots matters. The first rank appears at the top, and the last rank appears at the bottom. If the voter does not provide at least one rank, the ballot is counted as an entry of Support for a candidate "none of the above" and an entry of Oppose for each human candidate.
Each rank includes however many Candidate Entries as the voter chooses (but there should be at least one, and otherwise the rank does not count). The order of candidate entries in a rank does not matter. Each candidate entry fingers a candidate and also signifies one of the rating grades I give in the table at the top of this writing. If the rank is not the final rank on the ballot, each entry can also include an optional designation as Free. Iff a candidate entry is not marked Free, it is considered as Constraining.
The rank can also include a Default entry indicating how the candidates not explicitly named in candidate entries in the rank are to be treated. This can give any of the grades I list at the beginning of this article. The defaulted candidates are not in any case treated as though there were Constraining entries for them.
If the voter does not provide a Default entry, the system tries to calculate one. First, it averages the Constraining candidate entries found in the rank (arithmetic mean). If the result is strictly greater than zero, the default is Oppose. If the average is strictly less than zero, the default is Support. If the average exactly equals zero, the defaulted candidates’ scores are not affected (assuming 0 is in the middle of the range).
(If an interactive machine can be provided to conduct a dialog with the voter before her ballot is printed, it can warn in the case that the voter failed to specify the default and there are both explicit positive and negative entries).
The TallyTallying proceeds in a count of rounds that is one greater than the previously chosen count of virtual runoffs. Each round other than the first is a virtual runoff.
Each round of tallying starts out by initializing for each candidate an accumulator to zero. The round then examines the ballots.
For each ballot, we scan down the ballot through the ranks, starting with the first rank (which is at the top), and looking for a rank that qualifies to be counted in the round. We will count in the round from the given ballot, the first rank we find that qualifies, and only that rank. If no other rank qualifies, we will use the last rank. A rank qualifies exactly when all of the candidates mentioned in Constraining entries are still in the running, not having been eliminated by prior rounds of the tally.
After the round of tallying has examined all the ballots and updated the candidates’ accumulators accordingly, it looks for which candidates to eliminate. The candidates eliminated in the round should number approximately as the ratio of the number of candidates to the number of virtual runoffs, but at least one, but at most all but one. The round should eliminate the candidates having the lowest numbers on their respective accumulators.
The last candidate not eliminated wins. 
Appendix -- Notes and LinksPublic original of this post: https://wp.me/p23U97-hG
 Score Voting (also called Range Voting) https://electowiki.org/wiki/Score_voting
 Reweighted Range Voting: https://electowiki.org/wiki/Reweighted_Range_Voting
 If by popular demand the endpoints of the range were to be changed from -50 and 50 to 0 and 100, then the middle would be 50 rather than zero. In that case, if the voter gives no Default entry in a rank, and if the average of the Constraining entries in the rank were 50 (the new middle), then the defaulted candidates would get 50 from this rank when it is used in the tally.