When evaluating any decision purely in terms of the costs and benefits to yourself or to any single party—as opposed to the costs to you and the benefits to others in an act of altruism or reciprocity, you, of course, shouldn’t decide only on the basis of the benefits.
Huge benefits, but with comparably huge or even bigger costs, will not justify such a decision. That much is common sense. Less obvious is how we do or rationally should compare the costs and benefits of two conflicting decisions, e.g., the decision to hire Jack, or to hire Jill instead.
There are at least four ways to compare two job candidates, e.g., Jack and Jill, when thinking in terms of their respective total costs and benefits to a company:
- Estimate the difference between their cost-benefit ratios
- Estimate the difference of their cost-benefit differences
- Estimate the ratio of their cost-benefit differences.
- Estimate the ratio of their cost-benefit ratios
Among these, is there at least one rule that always leads to the right decision? Are there other rules that do a better job? Or is there no single rule that can guide cost-benefit-based decision-making in all cases? Whether you like doing this kind of arithmetic or not, you are probably going to do it—even if badly or intuitively. So you might as well get the concepts as well as the math right, and choose the rule that best fits your situation.
Different Cost-Benefit Calculations and Approaches
In a previous article, I created “M.O.R.E.S” as an acronym to describe five costs of recruiting: I identified “maintenance”, “opportunity”, “replacement”, “evaluation” and “search” costs as typical recruiter costs incurred in pursuit of employer and recruiter benefits. Salary, benefits, etc., may, for this purpose, be conceptualized as “maintenance”, or categorized separately as additional costs.
The “difference of cost-benefit ratios” approach involves comparing, as ratios, for each candidate, the quantified total costs and benefits associated with hiring him or her. That done, what remains to do is to calculate the difference between those two ratios. The second method requires first calculating the difference between the costs and benefits associated with each candidate and then calculating the ratio of those differences.
One very interesting question these three methods suggest is whether or not they can lead to different decisions about whom to hire. A second question is whether they involve substantially different ways of assessing a candidate. Clearly, if the answer to the second, more general question is no, the answer to the first must also be no. Similarly, if the answer to the first question is yes, so is the answer to the second question. However, a “no” in the first instance does not entail a “no” in the second, just as a “yes” in the second does not entail a “yes” in the first.
A third important question is what cost-benefit approach do or should we use, if we don’t use either of these. This includes consideration of what role, if any, marginal cost-benefit, rather than total cost-benefit approach, does or should play a role in hiring.
Some Examples and Applications
To keep things simple, let’s assume that these respective associated costs and benefits can easily be calculated, for the purpose of a hypothetical example and illustration for each approach: Imagine that hiring Jack will, over the cost of the contract, cost the company $100,000, but that the monetized pre-cost-calculated benefit to the company will be $500,000. Jill, on the other hand, will cost the company only $50,000, but generate benefits to the company worth only $250,000, exclusive of the costs.
Using the first method—the method of difference of ratios, we find that there is a zero difference between the cost-benefit profiles for Jack and Jill. Jack’s cost-benefit ratio is $100,000/$500,000, or 1/5. Jill’s is $50,000/$100,000, also 1/5. The difference between 1/5 and 1/5 is 0. Hence, as a decision method, the “difference of ratios” method and the associated decision rule, “Hire the applicant with the smaller cost-benefit ratio”, make the hiring decision a tossup between Jack and Jill. (A smaller cost-benefit ratio means that the costs are smaller than the benefits.)
Now apply the second method—the “difference of cost-benefit differences”. In this case, the benefit-cost difference in hiring Jack is $400,000 ($500,000-$100,000), while the B-C difference (benefits-costs) for Jill is $50,000 ($100,000 – $50,000). Clearly, using this yardstick, Jack is the better choice—the much better choice, since he will bring in $350,000 more benefit than Jill. So, does this mean we should always use the “difference of cost-benefit differences” approach to make the best decision?
No. Suppose your company has very limited funding and capital reserves, and is looking at two candidates, Hansel and Gretel. To hire Hansel will cost $100,000 per year and will generate benefits totaling $150,000 year (pre-cost, gross benefits). Gretel, on the other hand, will cost $50,000 per year and generate $100,000 in annual benefits.
In each case, the net benefit to the company will be $50,000 annually, so the difference of cost-benefit differences is $0, which falsely suggests the choice is a tossup for your company, when in fact it makes much more sense for a cash-strapped company to hire Gretel. Adding as an auxiliary assumption that costs should be minimized as a prime objective, the “difference of differences” approach becomes insufficient for making the right decision, or dead wrong in the absence of that minimization assumption.
Limitations and Uses of the Cost-Benefit Approaches and Rules
Thus far, it is obvious that neither the “difference of ratios” nor the “difference of differences” decision-rules will be effective, i.e., right in all cases. As argued, the difference-of-differences approach won’t work when minimizing costs is a very high priority; the difference of ratios approach won’t work when only the ratios, but not the absolute amounts (costs and benefits), are taken into consideration.
This does not mean that neither of these should ever be used. The difference-of-differences approach is excellent when the net benefit (after deducting costs) of hiring one applicant is bigger than that in hiring the other and when cost minimization is not a constraint. For example, if, despite affordable huge costs in hiring Bill Gates as an adviser, your company stands to make utterly gargantuan gains that dwarf the cost, it would be rational to hire Gates for that purpose, in accord with the difference of cost-benefit differences approach.
Likewise, using a difference-of-ratios approach that ignores the actual absolute cost and benefit amounts can make sense in some situations. For example, ratios can make a good measure of productivity—past, current and future. If one stock broker earns clients $100 million, but incurs losses equal to that, his 1/1 cost/benefit ratio hardly makes him a winner. A second broker who earns clients $50 million, while losing only $1 million has a much better C/B ratio of 1/50. Here, the cost-benefit ratios and the difference between them, viz., 1-1/50 (=49/50) clearly argue for the hiring of the second broker, purely on the basis of the ratios.
A Difference Between Ratios and Differences
A ratio of cost-benefit ratios will, in this instance, produce a similar result: The ratio of 1/1 compared with 1/50 yields a ratio of ratios that in benefit-cost terms is 50-to-1, thereby suggesting that hiring the second broker is fifty times smarter, i.e., that he will be 50 times as productive as the first broker. If you want your decision rule to be very sensitive to changes in ratios, then a “ratio of cost-benefit ratios” rule is recommended instead of a “difference of cost-benefit ratios”, since the former is non-linear, i.e., a more rapidly rising curve, whereas the latter is linear, i.e., is a straight line that rises or falls more gradually.
We all talk about “cost-benefit analysis” professionally or personally, yet usually very casually, without often doing the associated math or without employing an examined decision rule to guide our decision-making and our eventual decisions. That’s fine when costs are either negligible or equal, or, in some cases, when absolutely dwarfed by the benefits, but, otherwise, can be a huge mistake, e.g., using a “difference of ratios” approach with Jack and Jill, in the example given above.
The Idea of a “Best Rule”
The best rule to adopt in any concrete instance cannot be decided without factoring in the constraints on decision making, e.g., whether there is a tight budget for hiring or whether productivity matters more than total revenue generated when reviewing the candidacies of two brokers.
Now what remains for you to do is, in any concrete situation, to choose your approach from the initial four presented here (or others, such as marginal cost-benefit analyses) and to figure out which cost-benefit approach to use in trying to decide upon and justify which cost-benefit approach to choose.
In doing so, don’t forget to factor in as a cost the headache that exercise will probably give you.