When did lay people first get a vote in the general conferences of the United Methodist Church? In the news reports swirling around the 2019 General Conference of the United Methodist Church, something struck me as odd – there were "lay delegates" among the 800 delegates able to vote on the future direction of the denomination.  For example, NPR reported:


  Also speaking against the plan was Nancy Denardo, a lay delegate of western Pennsylvania (source)


Methodism was born out of the Church of England, which has an "episcopal" system of government – churches are led by priests and overseen by bishops.  It's a more hierarchical structure than Presbyterianism, for example, where churches are led by a group of elders and each church is overseen by all the elders in a particular region. 

But at least in my Presbyterian denomination, there is no concept of "lay delegates" at the general assembly – the only people who can vote are those who have been ordained as an elder/pastor.  Thus it seems odd to me that the Methodists – more hierarchical than Presbyterians – would allow the laity to vote in their general assemblies.

From my cursory research on Wikipedia, it sounds like the system today is not the way it was from the beginning – apparently the laity were denied voting rights at the 1792 General Conference, and a faction split from the church when laity were not given voting powers in the 1820s (source).

Thus my question is – when did the UMC, or its predecessor denominations, first allow laity to vote in its general conferences?

By predecessor denominations, I mean the Methodist Church (1939–1968), the Methodist Episcopal Church (1784–1939), and the Methodist Episcopal Church, South (1844–1939).
The first predecessor denomination to The United Methodist Church to allow laity to vote was  The Methodist Protestant Church, which did so when it was organized in 1830. In fact, the reason for the split from The Methodist Episcopal Church was over the issue of voting rights for the laity. Quoting from the Book of Discipline of The United Methodist Church 2016, 


  In 1830, about 5,000 preachers and laypeople left the denomination because it
  would not grant representation to the laity or permit the election
  of presiding elders (district superintendents). This new body was
  called The Methodist Protestant Church, which in 1939 united
  with The Methodist Episcopal Church and The Methodist Episcopal
  Church, South, to become The Methodist Church. [1]


Laity were granted voting rights by 1939 with the union of The Methodist Episcopal Church, The Methodist Episcopal Church, South, and The Methodist Protestant Church to form The Methodist Church. From the beginning of The United Methodist Church in 1968, when The Methodist Church united with the Evangelical United Brethren, laity have had voting rights in the General Conference and the Annual Conferences. 

There is apparently conflicting information in various editions of the Book of Discipline. Until the 2016 revision of the Book of Discipline, it is noted that The Methodist Episcopal Church did not grant voting rights to laity until the unification of 1939. The Methodist Episcopal Church, South, The Evangelical Association, and the Church of the United Brethren in Christ are noted as having granted voting rights to laity not later than 1932. 

Referring to the period between the American Civil War and World War I, the 2016 Book of Discipline contains the following passage: 


  Two other issues that caused substantial debate in the
  churches during this period were lay representation and the role
  of women. Methodist Protestants had granted the laity representation
  from the time they organized in 1830. The clergy in The
  Methodist Episcopal Church, The Methodist Episcopal Church,
  South, The Evangelical Association, and the Church of the United
  Brethren in Christ were much slower in permitting laity an official
  voice. It was not until 1932 that the last of these churches allowed
  lay representation.[2]


The earlier 2012 Book of Discipline indicates that The Methodist Episcopal Church granted voting rights to laity with the unification in 1939. 


  Two critical issues that caused substantial debate in the
  churches during this period were lay representation and the
  role of women. First, should laity be given .a voice in the General
  Conference and the annual conference? The Methodist Protestants
  had granted the laity representation from the time they
  organized in 1830. The clergy in The Methodist Episcopal Church,
  The Methodist Episcopal Church, South, The Evangelical Association,
  and the Church of the United Brethren in Christ were much
  slower in permitting the laity an official voice in their affairs. All
  finally granted lay people voting privileges in their General and
  annual conferences with the exception of The Methodist Episcopal
  Church, which did not grant this right in annual conference
  decisions before the 1939 union.[3]


There remain some restrictions on voting by laypersons. With the exception of lay members of specific committees, "lay members may not vote on matters of ordination, character, and conference relations of clergy." [4] This restriction has been in effect since the unification of 1939. 

References:


The Book of Discipline of The United Methodist Church 2016, p. 15-16. 
Book of Discipline, 2016, p. 19. 
The Book of Discipline of The United Methodist Church 2012, p. 18. 
Book of Discipline, 2016, Paragraph 33, p. 36.