William Thomson, A Pioneer of Mechanism Design and Fairness

I was introduced to the "uniform rule"[1] by my Professor William Thomson at Rochester in 1991-92 and was immediately fascinated by Sprumont's (1991)[2] characterization of the uniform rule, which shows that it is the only "non-manipulable" (see the next paragraph) allocation mechanism that satisfies Pareto efficiency and anonymity when individuals' preferences are "single-peaked".

Preferences are usually assumed to be convex in economics and single-peakedness is one such assumption. In mechanism design, it is typical to assume that the exact preference of an individual is private information, i.e. unknown to other individuals, including the mechanism designer. Nevertheless, mechanism designers can overcome such an asymmetric information problem by identifying mechanisms that are non-manipulable, i.e. incentives are provided by structured mechanisms to make truth-telling a dominant strategy for all individuals.

While information asymmetry and incentive compatibility are important aspects of mechanism design, a question dear to the heart of the public is whether "fairness" is served by the mechanisms or not. Mechanism designers should not shy way from this question and William has not. William is a pioneer of and has committed his career to mechanism design and fairness.

William recognizes that there is no unique notion of fairness and contributes to several formulations of it, including but not limited to, consistency (the shares allocated to others should not be affected by an individual leaving the group with his allocated share), resource monotonicity, population monotonicity and replacement principle (solidarity is the common theme of the last three formulations).

When William applied the above formulations of fairness to Sprumont's allocation problem, he obtained a number of alternative characterizations of the uniform rule.[3] The central role of the uniform rule in the literature was established by William and has subsequently been reinforced by numerous researches. I am privileged to take part in the formation of the literature.

The uniform rule is now applied to the real world. The Hong Kong Government started to issue iBond[4] in July 2011 and the inaugural issuance was oversubscribed. The HK Government decided to issue a maximum of HK$10 billion[5] iBond before receiving a total of HK$13.16 billion subscription from 155,835 subscribers. The uniform rule was used to allocate the iBond to the 155,835 subscribers as follows:

"[A]mong all the valid applications, those who have applied for 44 units or less will be allocated the full amount of bond applied for. There are a total of 150,869 such applications. In addition, there are 4,966 valid applications that have applied for more than 44 units. Each of them will be allocated 44 units first, and 1,344 of them will be allocated one additional unit of bond based on ballot results."[6]

In the two subsequent issuances of iBond by the HK Government (May 2012 and May 2013), oversubscriptions were received again. The uniform rule remained to be the allocation mechanism in both cases. The fourth issuance of iBond is on the way, and so will be the uniform rule.

William is a pioneer of mechanism design and fairness. One of his babies, the uniform rule, has made its way to the real world. The overdue of the uniform rule manifests that William is way ahead of many others. The dues of his other babies are uncertain. One thing is sure, though. When more of his babies are born, the world will be very different.

[1] See the seventh paragraph for a real-world example illustrating the uniform rule.
[2] Yves Sprumont, "The Division Problem with Single-Peaked Preferences: A Characterization of the the Uniform Allocation Rule," Econometrica, Vol. 59, No. 2 (March 1991), pp. 509-519.
[3] William Thomson, "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Volume 63, Issue 2 (August 1994), pp. 219-245; "Resource-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Social Choice and Welfare, Volume 11, Issue 3 (July 1994), pp. 205-223; "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Volume 5, Issue 2 (1995), pp. 229-246; "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Volume 76, Issue 1 (September 1997), pp. 145-168.
[4] iBond is an inflation-linked bond, similar to Treasury Inflation Protected Securities (TIPS) in the US.
[5] The exchange rate between US Dollar and HK Dollar is US$ 1 = HK$ 7.8.
[6] See http://www.hkgb.gov.hk/en/news/press_20110726.html.

控開支 促經濟 防財赤

香港政府的財政狀況目前十分健康。2013-14 財政年度的總收入估計為4478 億元，總開支4358 億元，入足敷支，為政府帶來120 億元盈餘，更令財政儲備升至7459億元。

《基本法》第107 條規定「香港特別行政區的財政預算以量入為出為原則，力求收支平衡，避免赤字，並與本地生產總值的增長率相適應」。

政府的財政預算是否符合《基本法》第107 條，不能單憑2013-14 年度（或其他單一年度）的財政表現來定斷。

香港於1997 年7 月1 日回歸中國，《基本法》亦同時生效。回歸初期，香港先後經歷亞洲金融風暴、科網爆破和沙士爆發，經濟大受打擊，政府收入隨之下降，財政赤字先後出現於1998-99 年度（亞洲金融風暴）、2000-01 至2003-04 連續四個年度（科網爆破及沙士爆發）。

嚴控開支 當務之急

面對如此嚴峻的考驗，港府仍能扭轉劣勢，轉赤為盈，令財政儲備自2004-05年度起連續上升，累積至現時的7459 億元，比1997-98年度的年終財政備多2884億元。

如果綜觀1997-1998 至2013-2014共十七個年度的財政數據，政府理應已符合《基本法》第107條中「力求收支平衡，避免赤字」的規定，體現「量入為出」的原則。

然而，政府的財政預算是否完全符合《基本法》第107條，還要看她是否與本地生產總值的增長率「相適應」。

在過去的十七個財政年度，政府總收入和名義本地生產總值分別累計增長59.2%和54.6%，兩者相若；政府總收入可謂與名義本地生產總值的增長率「相適應」，可是兩者卻遠遠低於同期的政府總開支累計增長124.2%，政府總開支實在說不上與名義本地生產總值的增長率「相適應」，有違《基本法》第107條之虞。

上述問題十分嚴重，當務之急是嚴格控制政府開支。財政司司長曾俊華亦意識到問題嚴重，在2014-15 年度《財政預算案》中，他建議削減政府總開支至4209 億元（比去年少149 億元）。此建議符合《基本法》第107條精神。

曾司長的建議成效如何，2014-15 年度《財政預算案》有以下的預測。1997-98 至2014-15 共十八個年度的政府總開支累計增長111.5%，同期的政府總收入和名義本地生產總值分別累計增長52.9%和61.5%；前者依然與後二者有很大的距離，問題尚未解決，司長仍須努力。

如果司長不繼續努力控制開支，政府的財政狀況將會惡化。長遠財政計劃工作小組（長計小組）甚至預測，結構性財政赤字必然會出現。長計小組推算政府的財政狀況於2014-15 至2041-42 年度期間的變化，期間的實質本地生產總值假設為平均每年增長2.8%。長計小組以下的兩個「基本情景」推算值得參考。

根據長計小組的推算，如果政府服務水平按歷史趨勢增長，政府總開支的平均每年增長率為7.5%； 結構性赤字將於七年後（2021-2022 年度）出現，財政儲備更會於之後的十年（2031-2032年度）耗盡，跟着政府便要借貸度日。

長計小組另外推算，如果政府維持現有服務水平不變，政府總開支的平均每年增長率將下降至5.3% ， 結構性赤字延遲至2029-2030 年度才會出現， 財政儲備更可維持至2041-42 年度。

按照長計小組的推算，雖然政府有足夠的財力維持現有服務水平不變，但結構性赤字仍會於2029-2030 年度出現，有違《基本法》第107條。

有見及此，長計小組集中向曾司長建議控制開支、增加收入和平衡收支。另一方面，長計小組卻完全沒有提出促進經濟增長的建議，只作出以下的推算。

假若實質本地生產總值平均每年增長3.1%（ 「基本情景」為2.8%），政府既可保持現有服務水平不變，又能避免結構性赤字出現。

延遲退休 不能治本

在作出上述推算後，長計小組卻指出「經濟的趨勢增長率難以大幅高於3%」。第一，3.1%不是大幅高於3%；第二，在過去五年，香港的實質本地生產總值平均每年增長3.9%，長計小組未免過於保守。

政府應有更闊大眼光，在加強財政管理之餘，還應促進經濟增長，雙管齊下方為上策。以下是一些促進經濟增長的建議：

一、取締退休年齡

隨着香港人口老化，勞動人口預計於2018 年開始減少，拖慢經濟增長。政府已提議延遲退休年齡，但此法治標不治本，任何預設的退休年齡均牽涉年齡歧視，而年齡歧視或其他歧視會妨礙求職、就業、晉升等等，要提升整體人口的生產力，政府應積極消除各種歧視，包括年齡、性別、種族，甚至族群，例如，政府應立法取締退休年齡，而不是把它延遲。

二、調整稅制，鼓勵生產

過去的十七個年度的財政數據顯示，政府收入和盈餘都跟隨經濟增長增加，經濟增長為政府帶來減稅空間。政府應調整稅制，使稅率和經濟增長掛；經濟蓬勃時，稅率自動調低。低稅率鼓勵生產，刺激經濟增長，再創造減稅空間，形成良性循環。

近年政府開支激增，遠超政府收入和經濟增長，有違反《基本法》之虞，長此下去，結構性赤字無可避免。面對如此嚴峻情況，政府不可單靠收緊財政管理，更應盡力促進經濟增長，雙管齊下，方可避免結構性赤字之餘，又不用削減現有服務水平。

 （刊於《信報》2014年5月9日http://forum.hkej.com/node/112742）