Abstract
While preparing this editorial I was in a transition state of moving house, which according to an article in the journal Plus 50 “appears with alarming regularity in lists tabling the ten most stressful life events.” 1 So everything is looked at, sorted out, and packed in boxes.
In a break I thought of my first editorial in the Journal of Integrative and Complementary Medicine in November 2021 that was on information technology and integrative medicine, where I talked about Semen Korsakovs invention of the homeoscope in the cholera pandemic in Russia in the 1830. 2 Now, looking at the situation of the world 1 year later, pandemics and Russia have reactualized in a somehow unpredictable way. On the first sight, there are two obvious and possible themes to talk about: COVID-19 and Ukraine. Although the first topic has been an ongoing subject in a variety of reviews and meta analyses in integrative medicine from a clinical perspective, 3 –5 I was unsure if and what to write concerning the latter case.
To get other thoughts, I started to pack boxes again, and oddly by chance I got hold of an examination from my student days 30 years ago at the University of Osnabrück on partial differential equations. The respective lecture was given by Horst Behncke, one of the most inspiring teachers in mathematical modeling I ever had the chance to meet. Apart from constructing mathematical models to answer questions such as “How long can a dachshund grow without its belly touching the ground?” (which by the way in a first approximation can be answered by modeling the flexural stiffness of the spine using the elastic beam theory), 6 he also introduced to us one of the most important findings of welfare economics: Arrow's impossibility theorem. So what does it say?
Kenneth Arrow, born about a century ago in 1921, stated and proved mathematically that it is not possible for a group of more than two voters and three or more alternatives A, B, C,… to have a group decision-making procedure that satisfies the following requirements for a social welfare function. 7,8
Universality
A voting ranks all options and the outcome is deterministic. There are no restrictions on which rankings are allowed. Each time preferences are presented in the same way, the same societal preference order occurs.
Independence of Irrelevant Alternatives
When option A is in front of B, A should still be in front of B, even if a third irrelevant option C is removed.
Positive Association of Social and Individual Values
If any individual changes a preference order by promoting an option, then the societal preference order should either promote that option in the new ranking or leave it at the same position. An individual should not be able to penalize a choice by increasing its preference.
Citizen Sovereignty
Every possible societal preference order should be achievable by some set of individual preferences.
Nondictatorship
A single voter cannot dictate a whole community. The social welfare function should account for the wishes of all voters.
Or in more easy words: it is impossible to fulfill the following (adapted from Nguyen et al
7
): If every voter prefers A over B, then the group prefers A over B. If every voter's preference between A and B remains unchanged, then the group's preference between A and B will also remain unchanged even if voters' preferences between other pairs such as A and C, B and C, or C and D change. There is no “dictator”: no single voter possesses the power to always determine the group's preference.
Kenneth Arrow in 1952 received the Nobel Prize for this impossibility theorem and perhaps this is more actual than ever. The COVID-19 pandemic still provides a unique opportunity to gather preference data in practice and to analyze them regarding Arrow's theorem, 8 and as Ross states, “to match policy with preferences.” 9 This, of course, might also be interesting when preferences of citizens voting for integrative medicine are considered, but to my knowledge this has not been picked as a research topic so far. For example, it might be interesting to investigate to what extent single voters do possess the power to determine a group's preference, for example, when looking at the present discussion on complementary medicine particularly in the field of social media as discussed in a recent article on media and science policy. 10
Apart from health and science policy issues, there is another idea, why is Arrow important for the field of integrative medicine? He is often credited as the founder of health economics, and indeed health economic evaluations might be the next cornerstone in the field of integrative medicine. Apart from conducting health economic studies, for example, in the treatment of back pain 11 or in a whole systems approach, 12 one can also use existing data from randomized controlled trials for a modeling approach, that is, using Markov chain models or other simulation techniques. 13,14 And indeed, literature for this area of research in integrative medicine is rising as shown in Figure 1.
Google scholar search for “cost effectiveness” and “integrative medicine.”
Unfortunately, however, the conclusion of Witt in 2011 still holds a decade after publication: “For valid decision making on complementary and integrative medicine, more clinical and health service research is needed which includes economic data to provide realistic cost estimates for future healthcare.” 15
Thus, there might be the right time for integrative medicine to have an Arrow in the quiver.