Equivalence of Stochastic and Deterministic Mechanisms

<jats:p>We consider a general social choice environment that has multiple agents, a finite set of alternatives, independent types, and atomless type distribution. We show that for any Bayesian incentive compatible mechanism, there exists an equivalent deterministic mechanism that (1) is Bayesian incentive compatible; (2) delivers the same interim expected allocation probabilities and the same interim expected utilities for all agents; and (3) delivers the same ex ante expected social surplus. This result holds in settings with a rich class of utility functions, multidimensional types, interdependent valuations, and in settings without monetary transfers. To prove our result, we develop a novel methodology of mutual purification, and establish its link with the mechanism design literature.</jats:p>

section_content: The Econometric Society (the "Society") holds that principles of professional conduct should guide all members of the Society, including, but not limited to, Officers, Council members, Editors, Co-Editors, Associate Editors and Data Editors of the Society's journals and monograph series and those serving on committees of the Society (collectively, the "Society Leadership"), Fellows and general members (the foregoing, together with the Society Leadership, the "Members"). Capitalized terms used but not otherwise defined herein shall have the meaning ascribed to them in the Society's Rules and Procedures dated October 2024 (as it may be amended, modified or supplemented from time to time, the "Rules and Procedures"). 

The ability of the Society to meet its Founding Purpose (as defined below) rests on its reputation, which depends on the reputation of the Society's Members. All Members of the Society are expected to abide by this Professional Code of Conduct (the "Professional Code of Conduct") and the Society's Conflict of Interest Policy (the "COI Policy," and, together with the Professional Code of Conduct, the "Code of Conduct") to the extent applicable, with Fellows and the Society Leadership members holding themselves to a heightened standard of conduct in their respective individual practice and professional capacity. Any Member of the Society who violates the Code of Conduct, to the extent applicable, may be subject to sanctions, including, but not limited to, as applicable, revocation of Fellow status, removal from all positions then held within Society and inability to renew membership, pursuant to the Society's Amended and Restated By-Laws dated October 2024 (as it may be amended, modified or supplemented from time to time, the "By-Laws") and Rules and Procedures. The Society's founding purpose of "the advancement of economic theory in its relation to statistics and mathematics" (the "Founding Purpose") requires intellectual and professional integrity. Integrity demands honesty, care, and transparency in conducting and presenting research; disinterested assessment of ideas; acknowledgement of limits of expertise; and disclosure of real and perceived conflicts of interest. 

The Society encourages the "freedom of economic discussion. " This goal requires an environment where all can freely participate and where each idea is considered on its own merits. All Members of the Society have a professional obligation to conduct civil and respectful discourse in all forums, including those that allow confidential or anonymous participation. The Society seeks to create a professional environment with equal opportunity and fair treatment for all Members and colleagues at the Society, regardless of age, sex, gender identity and expression, race, ethnicity, national origin, religion, sexual orientation, disability, health condition, marital status, parental status, genetic information, political affiliation, professional status, or personal connections. 

The Members of the Society shall treat other individuals in professional encounters with respect and shall adhere to their employers' codes of conduct or ethics and policies. Any form of discrimination 1, harassment 2 or bullying 3, including retaliation in any manner against a person who brings an alleged discrimination, harassment or bullying to the Society's attention or otherwise assists in the investigation thereto, violates the principles of equal opportunity and fair treatment, and as such constitutes an unacceptable conduct and a violation of the Professional Code of Conduct. Such unacceptable conduct shall include, but is not limited to:

1. Solicitation of emotional or physical intimacy despite expressions or indications that it is unwelcome. 2. Solicitation of emotional or physical intimacy accompanied by real or implied threat of personal or professional harm. 3. Intentionally intimidating, threatening, harassing, or abusive actions or remarks (both spoken and in other media). 4. Prejudicial actions or comments that undermine the principles of equal opportunity, fair treatment, or free academic exchange. 5. Deliberate intimidation, stalking, or following. 6. Harassing photography or recording. 7. Sustained or aggressive disruption of talks or other activities that undermine free academic exchange. 8. Physical assault (including unwelcome touching or groping). 9. Real or implied threat of physical harm. 

Appropriate principles of professional conduct also apply in the context of research and publication activities. Members of the Society are also expected to adhere to their employers' codes of conduct or ethics and policies that pertain to research. The following list of appropriate forms of conduct is unquestionably not exhaustive but illustrates some key principles:

1. Research should be conducted and reported with objectivity, accuracy, and high standards of quality. 2. Data, research methods and choices, and proofs should be discussed clearly in disseminated work and reasonable private requests for clarification and assistance should be engaged with in appropriate ways. 

1 Discrimination means prejudicial treatment of individuals or groups of people based on their age, sex, gender identity and expression, race, ethnicity, color, national origin, religion, sexual orientation, disability, health condition, marital status, parental status, genetic information, veteran status, political affiliation, professional status, personal connections, or any other characteristic protected by applicable laws.
section_name: Econometric Society Professional Code of Conduct

section_content: Harassment includes both sexual harassment and other types of harassment. Sexual harassment means unwelcome sexual advances, requests for sexual favors, and other verbal or physical conduct of a sexual nature that creates an intimidating, hostile, or offensive environment or is otherwise prohibited by applicable laws. Other types of harassment include, but are not limited to, any verbal or physical conduct directed at individuals or groups of people because of their age, sex, gender identity and expression, race, ethnicity, color, national origin, religion, sexual orientation, disability, health condition, marital status, parental status, genetic information, veteran status, political affiliation, professional status or personal connections that creates an intimidating, hostile, or offensive environment.
section_name: 2

section_content: acknowledged. In publications, presentations, and teaching, quoted material from another person's written work, published or unpublished, should be explicitly identified and credited. 4. If significant errors in publication or presentation of data or other work are discovered, these should be corrected as promptly as possible via a correction, retraction, or erratum. 5. Researchers should take responsibility and credit only for work they have actually performed and to which they have contributed. They should ensure that authorship and other publication credits are based on the scientific contributions of the individuals involved, regardless of their professional status. 6. In their roles as referees, researchers should review submissions carefully, confidentially, and without prejudice. Confidential submitted material should be kept confidential unless its release is allowed by the authors. Potential conflicts of interest should be construed broadly and discussed with the editor or conference organizer upon receipt of a request to review, and such editor or organizer should be informed of prior reviews of the same work. Referees should not use their advanced access to unpublished research for their own purposes. For example, they should not undermine the original authors by rejecting the paper and then pursue the research idea on their own. Nor should they delay providing feedback to the advantage of their own competing work. Referees should not reveal their identities to authors and should inform Editors if inadvertent revelation occurs. 

The Society Leadership members have an individual responsibility for their own conduct, and a collective responsibility to promote professional conduct. These responsibilities include developing institutional arrangements and a professional environment that promote free expression. These responsibilities also include supporting participation and advancement in the disciplines represented in the Society by individuals from all backgrounds, including particularly those that have been historically underrepresented. 

Any appointed or elected person in the Society who violates the Code of Conduct may be subject to sanctions including removal pursuant to the Society's By-Laws and according to the process described in the Society's Rules and Procedures.
section_name: Prior and contemporaneous contributions of other researchers should be clearly