Double random assignment with equal groups - vb.net

Question

I am trying to build a random sample and random assignment generator for a website I am working on that is supposed to assign randomly selected items in an equal number to a variable set of people.
For example:
In this round of assessment, we have 9 assessors, and 477 items that need to be graded by two assessors each (with the same assessor not grading the same item twice). This would come out to 954 total "assessments" that need to be made, and 106 per assessor.
Therefore I'd need an eventual list like...
(Item, Assessor1, Assessor2)
(1, A, B)
(2, C, D)
(3, E, F)
(4, G, H)
(5, H, B)
(6, B, F)
.
.
.
And so on
I've found websites that can do random number generation and even some that can do random assignment over groups, but even then I am still finding situations where the same assessor will be grading the same item throughout the results.
I am less concerned about the inherent randomness and more concerned about making sure each result list has every assessor grading the same number of items without grading the same one.
I can usually get it to the point where I have it -close- and maybe one grader will be 1 or 2 more and another will be 1 or 2 less, but unfortunately it's a hard requirement that they be equal groupings.
EDIT
Implemented #Tinstaafl's code and ran the following:
Dim col As New MyItemCollection
col.AddAssessor("A")
col.AddAssessor("B")
col.AddAssessor("C")
col.AddAssessor("D")
col.AddAssessor("E")
col.AddAssessor("F")
col.AddAssessor("G")
col.AddAssessor("H")
col.AddAssessor("I")
For I As Integer = 1 To 477
col.AddItem(I.ToString)
Next
Dim newList As List(Of MyItemCollection.MyItem) = col.AssignAssessors
For Each item As MyItemCollection.MyItem In col.itemlist
Response.Write(item.ToString & "<br/>")
Next
Unfortunately my output looks like
1 - F - F
2 - I - I
3 - E - E
4 - F - F
5 - C - C
6 - D - D
7 - G - G
8 - A - A
9 - C - C
10 - B - B
11 - D - D
12 - D - D
13 - D - D
14 - D - D
15 - H - H
And so on...

Answer 1

One idea that I can think of is as follows:
Shuffle the assessors {1-9}. Then assign the first 4.5 items to them sequentially as per the result of this shuffle.
Then shuffle them again. Again assign them sequentially to the next items. If the first assessor happens to be the same one that is already assigned to the 5th item, then swap the 1st and second assessor in the list.
Keep doing this for all items.

Answer 2

One way is with a collection class and embedded classes for the items and assessors. Here's a partial implementation to show how the list could be generated:
Public Class MyItemCollection
Class Assessor
Public Name As String = ""
Public Shared Operator <>(LH As Assessor, RH As Assessor) As Boolean
Return LH.Name <> RH.Name
End Operator
Public Shared Operator =(LH As Assessor, RH As Assessor) As Boolean
Return RH.Name = LH.Name
End Operator
Public Overrides Function ToString() As String
Return Name
End Function
End Class
Class MyItem
Public Name As String = ""
Public Assessor1 As New Assessor
Public Assessor2 As New Assessor
Public Overrides Function ToString() As String
Return Name & " - " & Assessor1.ToString & " - " & Assessor2.ToString
End Function
End Class
Private AssessorList As New List(Of Assessor)
Private ItemList As New List(Of MyItem)
Public Sub AddAssessor(Name As String)
AssessorList.Add(New Assessor With {.Name = Name})
End Sub
Public Sub AddItem(Name As String)
ItemList.Add(New MyItem With {.Name = Name})
End Sub
Private Rnd As New Random(Now.Millisecond * Now.Day * Now.Minute)
Public Function AssignAssessors() As List(Of MyItem)
Dim OutVal As New List(Of MyItem)
Dim average As Integer = ((ItemList.Count \ AssessorList.Count) * 2) + 5
Dim AssessorCount(AssessorList.Count - 1) As Integer
For Each item As MyItem In ItemList
Dim firstassessorindex As Integer
Do
firstassessorindex = Rnd.Next(0, AssessorList.Count)
Loop Until AssessorCount(firstassessorindex) <= average
item.Assessor1 = AssessorList(firstassessorindex)
AssessorCount(firstassessorindex) += 1
Dim secondassessorindex As Integer
Do
secondassessorindex = Rnd.Next(0, AssessorList.Count)
Loop Until AssessorList(secondassessorindex) <> item.Assessor1 AndAlso AssessorCount(secondassessorindex) < average
item.Assessor2 = AssessorList(secondassessorindex)
AssessorCount(secondassessorindex) += 1
Next
OutVal = ItemList
Return OutVal
End Function
End Class
One thing that wasn't clear in your explanation was if the distribution between Assessor1 and Assessor2 is important(does it matter if an assessor is the second assessor more times than it is the first?). If you need that, then a List(Of Tuple(Integer, Integer)) might be needed for the AssessorCount instead of a List(Of Integer)
The ToString method for each item in the return list will be in the format -
ItemName - Assessor1Name - Assessor2Name

Answer 3

I'm not sure if I understand your assignment rules, but this might be close.
var assessors = new []
{
"A", "B", "C",
"D", "E", "F",
"G", "H", "I",
};
var rnd = new Random();
var query =
from a1 in assessors
from a2 in assessors
where a1 != a2
orderby rnd.Next()
select new { a1, a2};
var results =
Enumerable
.Range(1, 477)
.Zip(query
.Repeat(),
(i, aa) => new
{
Item = i,
Assessor1 = aa.a1,
Assessor2 = aa.a2,
});
I get this kind of result:
1 F B
2 E C
3 D H
...
476 F C
477 B E