“In the CVS (Conventional Voting System), the input to the voting system is the preference order of a voter and each voter has a single vote. In the FVS (Fractional Voting System), the input is the preference distribution of a voter for the candidates ….”—K.K. Nambiar, School of Computer and Systems Science, Jawaharlal Nehru University, New Delhi, 1989

Fractional Ballot

FRACTIONAL BALLOT/Image: Michael Moffa

With the 2012 presidential election looming, the political focus will increasingly turn to voting and votes, with candidates vying for and trying to garner votes. Like voters in the upcoming primaries and election, recruiters have to study their candidates and “vote” for the one or ones who they believe will best get the job done.  However, unlike the citizen voter, recruiters have to do this every day.

A Different Way of Choosing Among Candidates

This aspect of any analogy between presidential elections and job candidate selection is obvious enough: You vote for the candidate you feel deserves your support. However, what is less obvious is the possibility that both presidential elections and recruiting could be improved by changing the way in which votes for the candidates—in both arenas—are cast and tallied.

As it stands, presidential and other job candidates either get your vote or they don’t, which, of course, is tantamount to giving one of them 100% support and the other none at all—an outcome that is unlikely to reflect your true, almost certainly at least mixed, measurably ambivalent sentiments about any given candidate or nominee.  Such traditional black-and-white, 0 or 1, yes-no voting is very binary and, because of advances in digital voting technology, ironically and paradoxically has perhaps become an anachronism in this hyper-digital binary age.

It is ironic and paradoxical, because, at this digital juncture with push-button voting machines, it is worth considering a shift to an analog format—a continuous, rather than discrete, measure of support, in the form of  very precise fractional or decimal ( terminal LED screen) voting for any candidate, irrespective of whether he or she is running for public office or merely being interviewed in yours.

Like Free Spending, More Precise Choosing

After all, if you are not forced to spend all of your dollars as votes for one product or service, why should you be required to spend all of your vote on one candidate? To be forced to allocate 100% of your voting assets, viz., your one vote, on one candidate is no different from being compelled to allocate every dollar to only one purchase. It’s also like monogamy.

What this means is that instead of a binary yes-no decision for each candidate on your short list, you apportion to each a fraction, decimal or percentage of your single vote, say 2/5 or 40% for Candidate X, 1/4 or 25% for Candidate Y and 7/20 or 35% for Candidate Z. This is one version of what is called a “Fractional Voting System” (FVS), in contrast to the Conventional Voting System (CVS), which allows no splitting of your single vote.

In this  FVS system, your clients can avail themselves of a far more sensitive measure of  your sentiments regarding the goodness-of-fit for each of the candidates you are seriously considering or recommending. (Since decimals and percentages are more convenient than and easily derived from fractions, they shall be used throughout the following discussion.)

Relative vs. Absolute Support

Of course, such fractional apportionment represents relative, not absolute support. A fractional vote, like the conventional yes-no vote, does not reveal how enthusiastically you’ve voted for someone, just as a simple ranking in order of preference does not. It represents only how much more you favor Candidate X over Candidate Y.  This is your “preference” for the candidates, not their “prominence” in your judgment. The candidate you voted for might be, for you, the least of the various evils, the lesser of two, the better of the two, or the best of the best.

Nonetheless, your individual fractional/decimal vote can embody and express the precise relative and comparative sentiments you have for any candidate in any kind of selection or election process vis-à-vis his or her rivals.  You may be inclined to respond, “But, I can already express myself precisely, by ranking each candidate on a zero to 10 scale. Why would I need to replace that with fractional/decimal FVS scoring or ‘voting’ method?”

Why One-to-Ten Doesn’t Cut It

The answer is this: The conventional zero to 10 scale doesn’t force you to choose among candidates the way the FVS does, since each ten-point scale score is independent of all the other scores, e.g., if you give one candidate a score of 10, you can still give each of the others the same score or any other score you wish to, within the zero to 10 range. However, when you vote fractionally or decimally, the more one candidate gets, the less that remains for the others, a forced tie being the only way in which equal scores are possible. It’s the difference between divvying up an infinite pizza and a conventional one. With an infinitely large pizza, each recipient can be given as many slices as you wish to give him or her; with the normal finite and FVS pizza, more for one means less for another, unless, in the special case, your choice forces a tie.

Hence, you are forced to even more carefully screen and recommend any given candidate, in a way that is not required by independent scores for the candidates. Think of this FVS approach as a kind of “zero-sum” game, in which one player’s gain is another’s loss—except that, in this instance, it’s more like a “1-sum” (“normalized”, as mathematicians would describe it), since all the scores or votes add up to 1 or 100% (depending on whether they are decimals or percentages).

Benefits of Zero-Sum Fractional Choices

Such a shift to fractional voting and recommendation would accomplish a number of good things: First, it would stimulate greater voter and recruiter reflection and awareness of their decisions and of the issues and factors. This is very good for fostering greater insight into the candidates, the issues and voter preferences. That’s very good for democracy, clients and pollsters.

That’s because in CVS conventional recommendations and voting, a vague feeling that Candidate X is better than Candidate Y merely has to reach a threshold for the vote to be cast for that candidate. But with FVS fractional or decimal voting and recommendations, there is obligatory consideration of how much better Candidate X is than the alternative candidate(s).  In your office, this system translates into more enlightened and insightful decision-making for you.

Moreover, fractional/decimal voting and recommendations better align the sentiments of the individual voter with those expressed by the entire electorate (in politics) or all demand-side stakeholders (in job placement, e.g., client, recruiter and supervisors). Since your company or client is, in virtue of having the final say, like the Electoral College, your fractional vote, like the popular vote’s  candidate vote ratios (e.g., 60%/40%) or differences (e.g., 20%, , 4 million votes), provides much better guidance and input than would a simple “win-lose”, “100%-0%”, “yes-no” for your job candidates or presidential candidates.

Push-Button Simplicity

The way this revised voting/recommendation scheme would work in the ballot box is the way it would work in your office: The voter (or you) would key in a two-digit number for each of the rival candidates, including 3rd- or 4th (etc.)–party candidates, e.g., “47”, “13”, “22”, “2” for each of four (or more) candidates (or as decimals, e.g., 0.47).

Because each voter or recruiter is allotted 100 percentage points to allocate as he or she sees fit, and because abstaining from voting for or recommending a given candidate can be allowed for those who can’t make up their minds about some specific candidate, e.g., because of insufficient information available on decision day, the sum of the allocated  and utilized percentages will not have to total 100.

In his 1989 research paper, titled “Arrow’s Paradox and Fractional Voting System”, in which K.K Nambiar endorses the replacement of the Conventional Voting System (CVS) with a variant form of Fractional Voting System (FVS), unused votes (here, unused fractions of single votes) are called the “anarchy” vote, which comprises passive-aggressive protest non-votes—in the present discussion, also non-voting due to uncertainty.

(One key difference between this analysis and Nambiar’s is the much greater mathematical complexity, mathematical rigor, profundity and refinements in Nambiar’s. A second difference is Nambiar’s analysis is based on allocating more than one vote per person, rather than on the kind of fractionalization of a single vote proposed here.)

What matters is that in the FVS 100 “points” are available, but on the condition they be divided up by you or the voter among the candidates, without any requirement that they all be used—again, to allow for the situations such as the one in which there is insufficient information or documentation for a given candidate or dislike for the slate of candidates.

Hence, if you are down to two candidates about whom you are lukewarm, you can give one 35 and the other 20 (or 0.35 and 0.20, if you have to key in the decimal point), and withhold the rest in connection with a third candidate. On the other hand, you cannot give both 90 (0.90), since the total cannot be more than 100 (1.0). If you think they are both outstanding and like them equally, the maximum will be 50% or 50 points (0.50) each.

Blending Preferences and Enthusiasm

But wait! If 50-50 means full marks for both, how is a lopsided score like 80-20 to be interpreted? This is not the numerical statement of the “enthusiasm”, absolute interest mentioned above. In both conventional yes-no voting and in fractional/decimal voting, only relative—not absolute—preferences can be expressed. So, how can both relative and absolute preferences be expressed in a single number?

Simple: just multiply each fractional/decimal relative ranking score by a number from 0 to 10, which can serve to represent the absolute level of enthusiasm. For example, suppose you preference-rank two candidates as  80% and 20%–working, in this illustration, with the model that says all points and percentages must be allocated (as opposed to the alternative model proposed above, which allows withholding a portion of your vote).  Now, multiply the decimal versions of each of these, viz., 0.80 and 0.20 by their respective “enthusiasm” scores, which will, of course be the highest for your first choice, unless there is a tie.

So, assume you give candidates X and Y enthusiasm or “prominence” scores of 7 and 3 respectively. The results will be 0.80 x 7 and 0.20 x 3, which equals 5.6 and 0.60,  respectively, This combined weighted result provides much more information than the conventional “X-Yes”, “Y-No”, “Z-No” ever could. Specifically,  it tells you that your overall support for Candidate X is 9.33 times your support of Candidate Y—which tells a client a whole lot more than “I prefer and recommend Candidate A over Candidate B.”

In a presidential election or in polls, such data can provide invaluable indicators about not only “yea-nay” support, but also precise measurements of the degree and firmness of that support.

Because this is simple and automated arithmetic, no mathematical skill is required. All that is necessary is, in the voting booth, to punch in two numbers for each candidate—the first number being the relative fractional/decimal score and then the second number, the absolute enthusiasm, prominence score. The machine will then multiply them to calculate your level of total support for each candidate. In your office, a simple pocket calculator stands in for the voting machine.

School Grades: a Bad Model for the Office

It may be retorted that the enthusiasm score should be enough, since it captures net sentiment on a scale that is more precise than the yes-no vote, just as the fractional/decimal voting system does. The counter-argument to this view has already been stated: because a 0 to 10 scale allows full marks for all candidates, with comparisons of them as a consequence, not a cause of the scoring, it does not require the kind of obligatory prior careful comparison and reflection that the FVA fractional/decimal scheme does.

What makes voting and recommending candidates different from marking exams (after which comparisons of those rated and graded can also be made) is that in recruiting and U.S. elections, unlike exams, not everyone can pass. There are no coalition governments in the U.S. and there are not multiple hirings for one job opening.

This special constraint adds another dimension of evaluation and decision beyond that based on school exam raw scores and rankings derived from them. Unlike school exam marking, voting and recruitment recommendations represent a zero-sum game: If one candidate wins, another must lose. Not so in school. Theoretically, everybody in a class can get an “A”.

S = R x A and a Caveat

The proposed weighted decision formula for a single candidate,  S = R x A, in which S represents the overall degree of support, R the degree of relative support and A designates the “enthusiasm”, absolute support factor, is as easy to use as it is to remember.

But note this: If I apply this formula outside the domains of elections and recruiting, e.g. if I compare this article with others I’ve written in my lifetime, for the purpose of ranking and recommending one of them, I’d have to say that S is close to zero, even though I love each and every one of the articles I’ve ever published. Now why is that? That’s because I’ve written hundreds.

So, assuming uniform quality of my writing, no single article among the hundreds will dominate the scoring and none will get more than a pizza percentage-point or two or significantly higher “A”, a.k.a., “enthusiasm” or “prominence” scores (with prominence, in this discussion, being a measure of the absolute intensity of support.

The “R” factor is necessary, because even though the FVS relative-preference factor “A” presented here allows you to say that you like Candidate X 2.6 or 9.33 times as much as Candidate Y, without the inclusion of “R” in the formula, there is still no measure of how much you like Candidate X, as a stand-alone, rather than in comparison with Candidate Y.  Bottom line: “A” and “R” complete each other.

The caveat in this observation and calculation is that this weighted FVS works best with a reasonably small number of candidates and, most importantly, should not be used to compare two or more candidate groups, e.g., one group ranked in the summer and another in the winter, unless the groups are of exactly the same size. That’s because if one group is much larger than another, the “S-scores” can easily be smaller for members of the former group than for those in the latter group, just because of the group size differences.

This caveat notwithstanding, given that your short lists are going to be short, this size limitation should pose no problem for you.

The only real challenge that remains is this: to get you, or at least the government, to actually try fractional voting.

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