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Power in Networks: The Medici

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Abstract

We use the Public Good (Power) Index and the Public Value to rank the marriages of business relations of 15 elite families in fifteenth century Florence—with a focus on the networks of the Medici and the taking of power by Cosimo de’ Medici. Theoretical analysis supports the outstanding position of the Medici family and explains much of its historical success.

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Fig. 1

Source: software package netrankr with file florentine_m (see. https://CRAN.R-project.org/package=netrankr). The Pucci family is not considered in the network scheme because this family had no marriage links to any other family. Table 1a in the appendix contains an alternative representation of the network in Fig. 1.)

Fig. 2
Fig. 3

(Source: software package netrankr with file florentine_m (see. https://CRAN.R-project.org/package=netrankr). The Acciaiuolli, the Albizzi, the Ridolfi, the Strozzi, and the Pucci family are not considered in the network scheme because these families had no business links to any other family. Table 2a in the appendix contains an alternative representation of the network in Fig. 3.)

Fig. 4

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Notes

  1. Machiavelli (1882[1532]: 197). characterizes Cosimo as “a man of rare prudence, of grace but agreeable presence, and most liberal and humane. He never attempted anything against the party opposed to him, or against the state, but endeavored to do good to all.” We will refer to Cosimo’s mode of decision making—labelled “robust action” by Padgett and Ansell (1993)—in the final section of this paper.

  2. See Max Weber’s definition of power discussed below.

  3. Machiavelli (1882 [1532]: 210) commented: “Thus did Florence, by this and similar proceedings, deprive herself not only of many good and worthy citizens, but of much wealth and industry.”

  4. Holler and Widgrén (1999) argue that the value of a coalition is power. More generally, v(.) is the characteristic function à la von Neumann-Morgenstern which assigns, in a cooperative game, values to coalitions.

  5. See Holler (1982a) for a discussion of this property. Because of the public good assumption, there is “no splitting up of a cake” and no bargaining over shares. Myerson (1977) presents a bargaining model for networks that connects the (fair) bargaining outcome and the corresponding Shapley value.

  6. The swing players define the power for the indices of Shapley-Shubik, Penrose-Banzhaf-Coleman, Johnston and Deegan-Packel. See Holler (1982b) and Holler and Nurmi (2013) for an extensive discussion of these measures.

  7. For a recent discussion of the PGI, see Holler (2019). Note there are more than ten power indices, but there is only one measure that is serious about measuring the impact of a player in producing a public good, i.e., the PGI.

  8. In the Medici world, various majority rules applied. The beauty of a majority rule is that when it comes to fighting—and quite often the sword was used to implement decisions—then it is more likely that the majority beats the minority. Voting signaled where the majority is—and, due to this information, the minority often gave in.

  9. In 1468, Lorenzo (Il Magnifico), although in love with Lucrezia of the Donati family, had to marry Clarice of the mighty Roman Orsini family. She is commonly characterized as a dull and quarrelsome woman. It seems that Lorenzo was not very happy with her. Still, they had a son Giovanni (1475–1521) who became Pope Leo X in 1513. It seems that the link to the Orsini was very helpful to the Medici family as in this period, during and after Savonarola (1452–1498), their position at Florence was repeatedly challenged by republican governments.

  10. This concurs with Max Weber’s definition of power: “In general, we understand by’power’ the chance of a man or of a number of men to realize their own will in a communal action even against the resistance of others who are participating in the action” (Weber, 1948 [1924]: 180). It seems that, in Florence, there was always a resisting party during the period of our analysis.

  11. In the Pazzi conspiracy of 1478, the threatened Medici and their supporters used their power (and the assistance of the people of Florence) to physically eliminate the Pazzi family and most of their allies—including the archbishop of Pisa. Exclusion did not work.

  12. For effects of a priori union on the PGI, see Alonso-Meijide et al. (2010a, 2010b).

  13. See Nurmi (2005) and Nurmi and Meskanen (2000), and the pioneering article May (1954) which is a straightforward application of Kenneth Arrow’s “Impossibility Theorem” (Arrow 1963 [1951]).

  14. See Overcast and Tullock (1971) and Tullock (1985) for pioneer papers.

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Authors and Affiliations

  1. University of Hamburg, and CCR-Munich, Munich, Germany

    Manfred J. Holler

  2. Kutaisi International University, Technical University Munich, and CCR-Munich, Munich, Germany

    Florian Rupp

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  1. Manfred J. Holler
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Correspondence to Florian Rupp.

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The authors would like to thank Benoît Le Maux, Hartmut Kliemt, Barbara Klose-Ullmann, Raymond Russ, and two anonymous reviewers for very helpful comments.

Appendix

Appendix

See Tables 1a and 2a.

Table 1a Marriage relations of 15 families in fifteenth century Florence
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Table 2a Business relations of 15 families in fifteenth century Florence
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Holler, M.J., Rupp, F. Power in Networks: The Medici. Homo Oecon 38, 59–75 (2021). https://doi.org/10.1007/s41412-021-00108-1

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