David,

I have developed a macro that does just that, though it does not optimize meeting attendance. By
that I mean, if a lot of people choose one specific meeting or class as their #3 choice, it will not
preferentially select those folks just to fill up the class - that is a judgement call on your part.
This is strictly based on attendee preferences, randomized to make it fair.  To optimize class size
or to fill up other classes, you may need some manual intervention.

Anyway, let's say that you have three meetings.

In cells B1:D1, enter the maximum allowed meeting size for the session.

In cells B2:D2, enter the meeting names. In E2, enter the word "Randomize" and in F2, "Assigned to"

Then in B3:D3, enter 0.  In cell E3, enter -1.

Then starting in A4, enter the name, and in cells B4:D4, the preference numbers.  In cell E4, enter
the formula =RAND()

Continue down columns A through D with the names and preferences, and copy the formula in E4 down
column E to match your database.

Then save it, and run the macro below.

Note that this can be expanded for as many meetings as you have by inserting extra columns before
the column with the =RAND() formulas.

If the participants can have more than three choices, increase the 3 of the
For myChoice = 1 To 3
to match the maximum number of choices.

If you want to manually fill meetings, enter the values in the "Assigned to" column.

If you have a problem, email me privately and I will send you a working example.

HTH,
Bernie
MS Excel MVP

Sub AssignToSession()
Dim i As Integer
Dim j As Integer
Dim myChoice As Integer
Dim myC As Integer
Dim myR As Range
Dim myV As Range

Set myR = Intersect(Range("2:65536"), Range("A2").CurrentRegion)

On Error Resume Next
ActiveSheet.ShowAllData

myC = Range("IV1").End(xlToLeft).Column

For myChoice = 1 To 3
  For i = 2 To myC
     myR.Sort key1:=Cells(2, i), order1:=xlAscending, _
              key2:=Cells(2, myC + 2), order2:=xlAscending, _
              key3:=Cells(2, myC), order3:=xlAscending, header:=xlYes

     myR.AutoFilter Field:=i, Criteria1:=myChoice
     myR.AutoFilter Field:=myC + 2, Criteria1:="="

     Set myV = myR.Columns(i).SpecialCells(xlCellTypeVisible)
     If Cells(1, i).Value > 0 Then
        If myV.Areas(2).Rows.Count < Cells(1, i).Value Then
           myV.Areas(2).Offset(0, myC - i + 2).Value = myR(1, i).Value
           Cells(1, i).Value = Cells(1, i).Value - myV.Areas(2).Rows.Count
        Else
           myV.Areas(2).Offset(0, myC - i + 2). _
              Resize(Cells(1, i).Value).Value = myR(1, i).Value
           Cells(1, i).Value = 0
        End If
     End If
     myR.AutoFilter
  Next i
Next myChoice

End Sub