Participatory Democracy with Imperfect Information Diganta Mukherjee Indian Statistical Institute, Kolkata 16th March 2016 Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 1 / 14 Plan 1 Introduction 2 The Benchmark Model 3 Optimisation 4 Extensions Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 2 / 14 Introduction The Setting The Aam Aadmi Party government on Saturday conducted public meetings in six constituencies of Delhi in the second phase of its participatory budgeting exercise. ... Going to the public for budget has helped the government understand local needs, which cannot be addressed from the Secretariat... said Dwarka MLA Adarsh Shastri. The Hindu, NEW DELHI, April 26, 2015 Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 3 / 14 Introduction Participatory democracy is a process of collective decision making Real life experiences: Brazilian municipalities, state level in Rio Grande del Sul (Brazil), in West Bengal and Kerala (India) (For details see Fung and Wright (2001)) Formal model of participatory democracy inspired by Aragone`s and Sanchez-Pages (2008): citizens decide whether to attend a meeting relevant for the final policy choice decide whether or not to reelect the incumbent politician Issues: uncertainty due to delegated participatory discussions inefficiency (lack of experience) in understanding and / or transmitting the policy choice of the electorate to the government Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 4 / 14 The Benchmark Model Electorate of unit mass. k local groups mass ni ; i = 1; 2; :::; k such that Pk i=1 ni = 1: Ideal policy choice for each group and governing party θ1; θ2; :::; θk and θ0 Delegates: Government officials or local level party workers Output: Unbiased but noisy signal, ai , of θi . Messengers operate independently 2 ai ∼ F (θi ; σ ) Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 5 / 14 The Benchmark Model Support function 2 2 S(θi ; θ^) = S((θi − θ^) ) = 1 − s(θi − θ^) Government's satisfaction function 2 2 D(θ0; θ^) = D((θ0 − θ^) ) = 1 − d(θ0 − θ^) Government's objective k X Π(S1; S2; :::Sk ; D) = Π( ni S(θi ; θ^); D(θ0; θ^)) i=1 k X = α ni S(θi ; θ^) + (1 − α)D(θ0; θ^) i=1 Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 6 / 14 The Benchmark Model Final choice of policy k k X X θ^ : wi ai + w0θ0; where wi ≥ 0 and wi = 1: i=1 i=0 ^ X 2 X 2 (θi − θ) ∼ F ((θi − wj θj ); σ wj ): Similarly ^ X 2 X 2 (θ0 − θ) ∼ F ((θ0 − wj θj ); σ wj ): P Denote E(θ^) = wj θj by θ. k X 2 2 2 X 2 E(Π) = 1 − [αs ni (θi ; θ) + (1 − α)d(θ0; θ) ] − [αs + (1 − α)d]σ wj (1) i=1 Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 7 / 14 Optimisation Optimisation with no uncertainty: σ2 = 0 Maximisation with respect to θ^ yields αs Pk n θ + (1 − α)dθ θ^ = i=1 i i 0 = θC ; say: αs + (1 − α)d Optimisation with uncertainty: Pk P θ2 P θ2 ^ αs i=1 ni θi + (1 − α)dθ0 j C j U θ = × 2 P 2 = θ 2 P 2 = θ ; say: αs + (1 − α)d (σ + θj ) (σ + θj ) Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 8 / 14 The optimal payoffs are: Certain C nX 2 C X C 2o C 2 Π = 1 − αs ni θi − 2θ ni θi + (θ ) − (1 − α)d(θ0 − θ ) (2) Uncertain U nX 2 U X U 2o U 2 E(Π) = 1 − αs ni θi − 2θ ni θi + (θ ) − (1 − α)d(θ0 − θ ) 2 X 2 −(αs + (1 − α)d)σ wj (3) Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 9 / 14 Figure 1 Figure: Preference geometry Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 10 / 14 Result Remark 1: (a) Payoff is decreasing in volatility. U C P 2 (b) Both E(Π) and Π are decreasing in ni θi , inter-group heterogeneity in the electorate. C 2 Both are also decreasing in (θ0 − θ ) . (c) Figure 1: The impact of distortion different for linear preference (with explicit presence of extreme groups). It will certainly hurt some groups (and/or the government). For a circular preference pattern, this may be mitigated automatically. Uncertainty ) distortion So interest of the incumbent: noise is reduced. Better delegation or more interaction. Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 11 / 14 Extensions Meeting cost c > 0 per capita. A−i 1 P A A−i A−i Notation θ = nj θj : So, (θ − θ ) = ni (θi − θ ) = the aggregate 1−ni j6=i signal from all other groups (except i th). αsn (θ − θA−i ) + αsθA−i + (1 − α)dθ αsn (θ − θA−i ) θC = i i 0 = i i + θC−i : αs + (1 − α)d αs + (1 − α)d Therefore 2 αsn (θ − θA−i ) (θC − θ )2 = i i + (θC−i − θ ) i αs + (1 − α)d i A−i Participation will be optimal if jθi − θ j greater than ηi Remark 2: (a) bigger groups participate more. (b) extreme groups always participate Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 12 / 14 Extensions Intra-group heterogeneity 2 Assumption: ai ∼ F (θi ; σi ) For moderate groups incentive for participation will be actually smaller. Extreme groups will all participate and with more vigour. Strategic behaviour Electorate indicating their choice as different from the true θi . For preferences on a line, reporting will be upward biased for groups with above average θi . A strategic filtering of the signals needed by the government. For preferences on a circle, If diametrically opposite: truth will become a dominant strategy. When closer: incentives for misrepresentation reappears! Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 13 / 14 Thank you Comments are welcome [email protected] Diganta (ISI) Participatory Democracy with Imperfect Information 16th March 2016 14 / 14.