Trade-off

The design for the Apollo Lunar Module involved a tradeoff in the number of landing legs. Three legs reduced the weight of the vehicle but was considered unsafe. Five legs was considered safest but were too heavy. Designers compromised on four landing legs.

A trade-off (or tradeoff) is a situation that involves losing one quality or aspect of something in return for gaining another quality or aspect. More colloquially, if one thing increases, some other thing must decrease. Tradeoffs can occur for many reasons, including simple physics (into a given amount of space, you can fit many small objects or fewer large objects). The idea of a tradeoff often implies a decision to be made with full comprehension of both the upside and downside of a particular choice, such as when a person decides whether to invest in stocks (more risky but with a greater potential return) versus bonds (generally safer, but lower potential returns).

The term is also used widely in an evolutionary context, in which case natural selection and sexual selection act as the ultimate "decision-makers". In biology, the concepts of tradeoffs and constraints are often closely related. In economics, a trade-off is commonly expressed as opportunity cost which is the preferred alternative when taking an economic decision.

Examples from common life

The concept of a tradeoff is often used to describe situations in every-day life. The old saying "do not put all of your eggs into one basket" implies a tradeoff with respect to spreading risk, as when buys a mutual fund composed of many stocks rather than only one or a few stocks. Similarly, trash cans can be small or large. A large trash can does not need to be put out for pickup so often, but it may become so heavy when full that one risks injury when trying to move it.

In cold climates, mittens serve well to keep the hands warm, but they do not allow the hands to function as well as do gloves. In a like fashion, warm coats are often bulky and hence difficult to store or even to hang up.

When copying music from compact disks to a computer, lossy compression formats, such as MP3, are used routinely to save harddisk space, but information is thrown away to the detriment of sound quality. Lossless compression schemes, such as FLAC or ALAC are a compromise solution.

Large cars can carry many people, but they also tend to be heavy (and often not very aerodynamic) and hence have relatively poor fuel economy.

In the Olympics, the best sprinters are not the same individuals as the best marathoners, a tradeoff based on various morphological, physiological (e.g., variation in muscle fiber type), and possibly motivational factors.

Tradeoffs in economics

In economics the term is expressed as opportunity cost, referring to the most preferred alternative given up. A tradeoff, then, involves a sacrifice that must be made to obtain a certain product, service or experience, rather than others that could be made or obtained using the same required resources. For a person going to a basketball game, their opportunity cost is the money and time expended, as compared with the alternative of watching a particular television program at home.

Many factors affect the tradeoff environment within a particular country, including availability of raw materials, a skilled labor force, machinery for producing a product, technology and capital, market rate to produce that product on reasonable time scale, and so forth.

Tradeoffs in other specific fields

In biology and microbiology, tradeoffs occur when a beneficial change in one trait is linked to a detrimental change in another trait.

Tradeoffs are important in engineering. For example, in electrical engineering, negative feedback is used in amplifiers to trade gain for other desirable properties, such as improved bandwidth, stability of the gain and/or bias point, noise immunity, and reduction of nonlinear distortion. The Golden Gate Bridge is a prime rare example where few engineering and aesthetic tradeoffs had to be made.

In demography, tradeoff examples may include maturity, fecundity, parental care, parity, senescence, and mate choice. For example, the higher the fecundity (# of offspring), the lower the parental care. Parental care as a function of fecundity would show a negative sloped linear graph.

In computer science, tradeoffs are viewed as a tool of the trade. A program can often run faster if it uses more memory (a space-time tradeoff). Consider the following examples:

• By compressing an image, you can reduce transmission time/costs at the expense of CPU time to perform the compression and decompression. (Another aspect of this tradeoff is the loss in image quality, which is more apparent when the image is viewed at larger sizes.)
• By using a lookup table, you may be able to reduce CPU time at the expense of space to hold the table, e.g. to determine the parity of a byte you can either look at each bit individually (using shifts and masks), or use a 256-entry table giving the parity for each possible bit-pattern, or combine the upper and lower nibbles and use a 16-entry table.
• For some situations (e.g. string manipulation), a compiler may be able to use inline code for greater speed, or call run-time routines for reduced memory; the user of the compiler should be able to indicate whether speed or space is more important.

The Software Engineering Institute have a specific method for analysing tradeoffs, called the Architectural Tradeoff Analysis Method or ATAM.

Strategy board games almost always involve tradeoffs. In chess do you trade a bishop for position? In Go, do you trade thickness for influence, and just when does the middle game begin?

The study of ethics can be viewed as a system of competing interests that must be traded off against each other. (Is it ethical to use Nazi science to prevent disease today?)

In medicine, patients and physicians are often faced with difficult decisions involving tradeoff. One example is localized prostate cancer where patients need to weigh the possibility of a prolonged life expectancy against possible stressful treatment side-effects (patient trade-off).

Governmental tradeoffs are among the most controversial political and social difficulties of any time. All of politics can be viewed as a series of tradeoffs based upon which core values are most core to the most people or politicians. Political campaigns also involve tradeoffs, as when attack ads may energize the political base but alienate undecided voters.

Other uses of the term "tradeoff"

In music, the term "tradeoff" can also refer to solo instruments that swap solo duties, such as musical groups with two lead guitarists, who both share guitar solos. The term is used frequently in heavy metal, where bands often feature "twin guitars", such as Iron Maiden, Judas Priest, Megadeth, and Slayer, all of which feature lead guitar song sections that may involve four or more "tradeoff" solos. A more limited number of bands, such as Dream Theater, also implement the tradeoff with keyboards and lead guitar.

Analytical methods to support a trade study

Trade studies are essentially decision-making exercises. In the FAA Systems Handbook. the decision analysis matrix (aka Pugh's method) is suggested to support the activities, but this method can not support uncertainty, a mix of quantitative and qualitative information, or teams. To manage uncertainty, the authors suggest supplementing point estimates of the outcome variables for each alternative with computed or estimated uncertainty ranges. The Standard Approach to Trade Studies, an INCOSE paper from 2004, suggests a similar approach.

In the NASA Systems Engineering Handbook NASA suggests using multi-attribute utility theoretic (MAUT) or the Analytic Hierarchy Process (AHP). But, these too are not good with uncertainty, mixed information and teams. The authors suggest using probability based methods to maximize utility when uncertainty predominates, but give little detail on how to approach this.

In many situations, linear programming methods like the simplex algorithm can be used but these too do not support uncertainty. Another approach to supporting trade studies with uncertain information is to use the Bayesian methods.

See also

• Architecture tradeoff analysis method
• Carrier's constraint
• Detection error tradeoff
• Evolutionary medicine
• Evolutionary physiology
• Patient trade-off
• Space–time tradeoff
• Time-trade-off
• Trade-off theory of capital structure
• Williamson trade-off model

Further reading

• Alexander, R. McN. 1985. The ideal and the feasible: physical constraints on evolution. Biol. J. Linn. Soc. 26:345-358.
• Bennett, A. F., Lenski, R. E. 2007. An experimental test of evolutionary trade-offs during temperature adaptation. Proc. Natl Acad. Sci. USA 104:8649-8654.
• Campbell, D. E., and J. S. Kelly. 1994. Trade-off theory. The American Economic Review 84:422-426.
• Haak, D. C., McGinnis, L. A., Levey, D. J., Tewksbury, J. J. 2012. Why are not all chilies hot? A trade-off limits pungency. Proc. R. Soc. B Biol. Sci. 279:2012-2017.
• Roff, D. A., Fairbairn, D. J. 2007. The evolution of tradeoffs: where are we? J. Evol. Biol. 20:433-447.
• Stearns, S. C. 1989. Trade-offs in life-history evolution. Functional Ecology 3:259-268.