For my Adults with Asperger's book group meeting, we were asked our choice for the next book to read and discuss. Some clear majority emerged, fortunately, otherwise the book group leader would have had to figure out some way of making the selection based upon our different choices. For whatever reason, they hit upon some ranked voting schema. To their credit, not surprising, whether to adopt ranked choice voting is one of the questions on the state ballot this year.
     If I were teaching in-person this year, then I certainly would have organised lesson plans on the mathematics of voting. Difficult give explanations without some visual aid, so I would have borrowed or constructed slides. More fun would be using some pre-fab Mathematica notebook.
     PBS have produced a series of videos on the topic of voting years ago and even referenced the, to date, the go to standard video on the topic made by a YouTube channel CP Grey. Rather good instructive videos they are.

     Of late, I have given some thought as to how I could explain without the convenience of a chalkboard, or even a whiteboard, say, in a dinner table setting.

     There are certain notions and aims we may want preserving when voting.
1. The common sense notion that the winner with the most votes should win.
2. Fairness: one person, one vote.
3. The choice made in voting should not depend upon the inclusion or removal of alternative option. Some address this as the 'spoiler effect'.

     A math paper published decades ago proved that no voting schema could possibly exist without violating at least one of these 'axioms'. To date, there exist five suggested voting schemes. Two of which are variation on another and one we practice already but comes plagues with problematic issues of its own.

     So what are the different voting methods?
1. Winner take all or first past the post.
     This is the simple, straight forward everyone votes and the winner is the person with the most votes.
     The problem with this approach is when there exists more than two options. Unless one option wins with at minimum 51% for a majority, no option will can be considered what the majority wants.
     Sorry, I am going to throw in some numbers for illustrative purposes.
     Again, unless an available option receives 51% of the votes, anything less no matter how much implies more voters did not want that option. Say, 50% voted for option A, that leaves, say, 25% for option B, 15% for option C, and 10% for option D; meaning more voters did not want option A even though option A won more votes than any of the alternatives.
     So here is the nuance. By limiting the available options to two choices only, there is a better chance of at least one of the two options receiving a majority. Along with other reasons, this is one as to why mainstream media tries suppressing third parties. The one notable exception is when acknowledging such served their interests such as against the incumbent president in the 1992 election.
     The idea is if there are only two choices. Everyone makes a choice between either A or B, with the implicit premise that an odd number of voters, then either one must win with a majority. What upsets this is when there are more than two options. Unless there is a definable favourite, receive $100 tax free or a poke in the eye, winning by 51% or more is not likely and the likelihood decreases with each additional option.

2. Run-off elections
     Come run-offs to the rescue. The idea here is taking the top choices and sparring them against each other. Borrowing from the numbers from the previous example, options A and B would be in a run-off election leaving out options C and D. In effect, the run-off election scheme forces a binary candidate options to make Winner-take-all viable. in other words in the abstract, run-off elections sieve off the top n number of vote getters to re-run the election with just those n options.
     This violates, principle #2. If some one voted either for options C or for D, they are not given the choice to vote for their options in the run-off election. Those who voted either for option A or for B have a second chance -- a second vote at choosing, for their  preferred option. Run-offs tend to disenfranchise those whose option loses out and disincentivized those from voting again, or even worst, they do vote but out of spite.

3.  Ranked Choice Voting
     Comes ranked Choice Voting to the rescue. Not.
     The scheme invites the voter to rank their preference of the options. The option with the fewest votes is dropped, and those who ranked that option first will have their votes of their second choice re-distributed to the remaining options.
     Aside from breaking #3, this method of voting is just an iterated run-off election scheme.

     A good example of this in real life politics is the presidential primary election process. The primaries are an iterated run-off voting scheme. With each primary election, the one who lands at the bottom drops out of the race, leaving the subsequent voters to choose among the remaining presidential candidates. This repeats state by state until there is a de facto majority, among the participating voters. Those who candidate did not make the final cut felt disenfranchise e.g. Millennial Bernie Sanders supporters (aside from other extraneous factors) or voted out of spite for alternative candidates e.g. never-Trump-ers (Republicans) who voted for Hillary Clinton.
     To be clear on one point some may take issue, in each primary election, the voters are not ranking their preference among the presidential candidates, but the aggregate results amount to as if all the primaries had happened simultaneously in every state and each voter had ranked their preferences.

     Aware of the impossibilities that Arrow's Theorem places on voting systems, some suggest variations on the previously established voting schemes. One such popular favourite is
4. Cardinal Ranked Voting
     The extra bit of difference is the idea of attaching weights or points to the rankings, in some instances by the voters themselves e.g. 'my preference is for option A at 60%, option B at 30%, and option C at -10%', or fixed by the election officials.
     The short rebuttal is cardinality reduces to ordinality. Ranked Choice Voting is an ordinal ranking scheme.

     Others still suggest
5. Proportional Voting
    In a sense, the United States has that process already in some variant, but it too is fraught with a whole set of other problems, most notable is gerrymandering.
     Proportional voting is not a good scheme when choosing a president; better applied to a the legislature branch. Germany's parliamentary system has this, and their parliament is composed in direct proportion to the political ideology of the populace. That makes so much sense to me. We, in the United States, can do similar with slight tweaking and can be done without tampering the Constitution.


     Speaking of tampering with the Constitutional, here I saved my political rant to the end, there is reoccurring push to change the (election) rules of the game because some are dissatisfied by the outcome.
     One prime example is the Electoral College. Even when introduced and continued throughout US History, there is much debate and drive at wanting to rid the EC. Seemingly evermore so now, as was in 1976 (?) was it when NACCP defended then, the losing party wants to abolish a system that seems to favour their opponents. Mark my words, if candidate Biden wins, all discussion of Electoral College reform or removal will be in abeyance; if Trump is re-elected, then the will double-down on their efforts.
     Since the introduction, and I shan't go into the history and long of it all, the short of it is the Electoral College was designed to compensate for the low population areas or the sparsely dense regions of the country. Without EC, presidential elections would be decided by California and New York with possible sometimes Texas and Florida. N.B. The double prong strategy of the Democrats of both campaigning to reform or remove the EC altogether while trying to transform Texas from a Republican-leaning state to a Democrat-leaning state. Once the Democrats win Texas, they have a lock on the Electoral College.
     The EC was conceived around and based upon their being a two-party system. As one who votes third party, one would imagine that I would favour, as flawed as such schemes may be, an(y) alternative that breaks from the two-party dominance. No.
     The system is neither broken nor antiquated. The system is designed to do what it was set out to do. Being old does not imply or presume being obsolete. Even with the knowledge of Quantum Mechanics, and understanding such as it is, Newton/Classical Mechanics is taught still because it works and applicable still in the real everyday world from building a house to landing something on Mars.
     This is part and parcel of what is meant to be Conservative. It is not about preservation of old traditions of halcyon bygone days. It is about not tossing out the baby with the proverbial bathwater, my disposition towards babies notwithstanding. It is about progress towards perfection; not revolution to some trendy zeitgeist thought to be (on the) 'right' (side of history).


     All this said, what is the answer to the question? There is no magic formula that can collate submitted votes so as to arrive at an optimum selection. There, however, is an alternative approach that may serve the purpose to greater degree, what I shall call for the moment, inverted voting. My choice in calling this novun organum, as it were, is really more of an analytic decision making calculus extended to apply multiple inputs.
I shall use a recent experience as illustration.
     A previous weekend, an out of state friend was revisiting, joined by a more local friend. What has happened in the past is not making plans on where to eat even though that was the main activity in our get together. So we end up usually wandering downtown Boston streets undecided on a place for dining. For their recent visit, I invited them to fashion a list of places they were keen on trying for dinner. Between my more local friend and myself, we were non-committal; but on the day of I had a craving for a particular cuisine not on my visiting friend's list, my local friend had imposed certain parameters regarding the location setting and dining options, and there were circumstances that delimited our choices on the list. Deciding upon where to eat became a filtering process of narrowing down until we determined the one best option.
     Now, if weights were attached to the parameters and a point value scheme associated with each evaluation of the option in regards to the parameters, then you have the making of an analytic engine that can determine, if not the best, the most preferred option. Problems of deciding what to read and for whom to vote for election becomes a matter of, to quote Leibniz, "Let's calculate". 

     A more illustrative example has us consider parameters such as fiction vs non-fiction, Asperger's themed or not, genre (e.g. mystery, romance, Western, sci-fi). Weights may given by voter ranking preference e.g. wanting to read a fictional work is preferred over reading non-fiction. Values in choice given, say for simple example, a scale 2 for 'yes', 1 for 'maybe', 0 for 'I don't care' and a -1 for 'no'. Imagine a spreadsheet, if you will, where along one column is a listing of all the parameters with associated value-weights along an adjacent column. The person evaluates each option against the weight parameters. The end result is a ranking of their choice according to their parameter preferences. Extend this to all involved in choosing, can compile the end results of everyone's evaluation thus leading an overall selection.
     Such a scheme works well when a collective is deciding upon where to eat, choosing a vacation local, or what book to read next. Can this process work for deciding who is president? Yes, . . . but . . . I foresee two problems. The solution to one requires finer parsing of the parameters to a greater granular extent. The second problem raises a philosophical debatable issue. At the moment, I imagine an interlocutor arguing, but is this not just ranked choice voting dressedd up in an analytic guise? They would be sort of correct — for the individuarl voter. Note the difference shifts the to ranking candidates against the issues rather than compareing candidates against each otehr. The real quandery araises in how to collect the individual scores.
     For intellectual integrity, I invite others challenge my idea.

     In another context, I addressed alternative modes of exercising democracy. The point there I was making is for a democratic republic, such as ours, there are multiple ways in which we can select our representatives some of whch do ot violate the Constitution; the electoral — ‘electoral’ as in election process not Electoral College, is only one of those ways, which may be regarded as antiquated especially in light of a mathematical proof that Plato demonstrated thousnads of years ago in his Republic is the current preferred known method.