# A participatory budget model under uncertainty

TL;DR: This paper proposes a model for participatory budgeting under uncertainty based on stochastic programming, and suggests that this approach seems lacking, especially in times of crisis when public funding suffers high volatility and widespread cuts.

Abstract: Participatory budgets are becoming increasingly popular in many municipalities all over the world. The underlying idea is to allow citizens to participate in the allocation of a fraction of the municipal budget. There are many variants of such processes. However, in most cases they assume a fixed budget based upon a maximum amount of money to be spent. This approach seems lacking, especially in times of crisis when public funding suffers high volatility and widespread cuts. In this paper, we propose a model for participatory budgeting under uncertainty based on stochastic programming.

## Summary (1 min read)

### 1. Introduction

- Most countries have a strict legal framework that regulates budgetary processes.
- Furthermore, the elaboration of flexible budgets requires the use of multiple tools and methods such as Monte Carlo simulation, forecasting or game theory models (Verbeeten, 2006) Section 5 illustrates their methodology with a simple example.

### 3. The case of a single participant

- Β would typically be stated by the technical staff supporting the process after listening to the problem owners concerning uncertainty aversion, with sensitivity analysis performed to assess its impact.
- The selection of this parameter is critical, since it will affect the number of choices available.
- In general, the lower β is, the bigger the number of feasible portfolios would be available but, also, the bigger chances of not meeting the specified targets.

### 4.1.1. Posting under uncertainty

- The authors assume that projects are ordered according to their expected utility and a simple bookkeeping mechanism is available to avoid repeating portfolios already declined.
- A participant may propose the portfolio ϝ where projects are gradually included when the proportion of samples satisfying the corresponding constraints is greater than β.

### Stop;

- (c) Approximate K(S, x) through the nondominated portfolio closest to the straight line joining x and B(S, x).
- The authors just need to replace the corresponding steps in Algorithm 7 (and eliminate its first line) to obtain a much more affordable algorithm.

### 4.3. Arbitration under uncertainty

- Method assumes an initial inefficient solution and suggests at each iteration, as new solution, a Pareto improvement with respect to the previous offer, see Raiffa et al. (2002) .
- The process ends when no further Pareto improvements are possible.
- Again, this assumes that uncertainty has been previously resolved after applying Algorithms 1-4.
- As this may be expensive computationally, the authors could apply a similar approach to the BIM under uncertainty algorithm in Section 4.1.2.

### 5. An example

- The final budget therefore includes the following five projects:.
- Bike lane, Park, School, Theater and Trees.

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##### Citations

79 citations

### Cites background from "A participatory budget model under ..."

...Theoretical studies have focused on communication, deliberation, and decision making [5], modeling under uncertainty [6], designing general frameworks [7], and experimental solutions [8], [9], but most of these existing solutions only consider support for administrative tasks related to PBs, rather than the actual decisionmaking process....

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17 citations

12 citations

7 citations

### Cites background from "A participatory budget model under ..."

...…(radio, television, press, the Internet, telephone networks) and through medium such as billboards, posters, audiotapes and video, CD-ROMs, etc. (Kotler & Keller, 2012); direct marketing - the use of post, phone, fax, e-mail or the Internet to communicate directly or encouraging specific…...

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...…- the use of post, phone, fax, e-mail or the Internet to communicate directly or encouraging specific recipients to a response and a dialogue (Kotler & Keller, 2012); events and experiences marketing - activities and programs organized by the municipality, which are aimed at daily or…...

[...]

...…municipality, which are aimed at daily or occasional interactions with recipients, including sports, cultural, entertainment, charity events, etc. (Kotler & Keller, 2012) and finally interactive marketing - activities and programs on the Internet, aimed at drawing the recipients into interaction…...

[...]

...…etc. (Kotler & Keller, 2012) and finally interactive marketing - activities and programs on the Internet, aimed at drawing the recipients into interaction and direct or indirect increase of awareness, improving the image, increasing the interest in the offer of municipality (Kotler & Keller, 2012)....

[...]

6 citations

##### References

2,335 citations

### "A participatory budget model under ..." refers background in this paper

...Two clasic versions of chance-constrained problems are the individual chance onstraints (Charnes & Cooper, 1959; Wets, 1989) and the joint chance onstraints (Miller & Warner, 1965), which we adopt here: we place a ower bound β on the probability that each stochastic constraint will e jointly…...

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1,855 citations

1,609 citations

### "A participatory budget model under ..." refers methods in this paper

...BIM under uncertainty BIM is an iterative multilateral negotiation support method, based n the discrete balanced increment solution, see Raiffa et al. (2002). tarting from the disagreement point d, the method iteratively ofers (Kalai & Smorodinsky, 1975) solutions to participants....

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836 citations

### "A participatory budget model under ..." refers methods in this paper

...We assume that we may model each participant’s preferences hrough a multiattribute utility function uj, j = 1, . . . , n, whose xpected value should be maximized, see e.g. French (1986)....

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641 citations

### "A participatory budget model under ..." refers background or methods in this paper

...For a general discussion on the role of uncertainty in negotiations see Raiffa, Richardson, and Metcalfe (2002), Neale and Fragale (2006) or Moon, Yao, and Park (2011)....

[...]

...BIM under uncertainty BIM is an iterative multilateral negotiation support method, based n the discrete balanced increment solution, see Raiffa et al. (2002). tarting from the disagreement point d, the method iteratively ofers (Kalai & Smorodinsky, 1975) solutions to participants....

[...]

...…Calculate bt = bt−1 − Ct ; xt = B−1(S, bt) and K̂t = K(S, xt); if K̂t = K̂t−1 then Offer alternative associated with K̂t ; ethod assumes an initial inefficient solution and suggests at each teration, as new solution, a Pareto improvement with respect to the revious offer, see Raiffa et al. (2002)....

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