1. Attribution – NonCommercial - ShareAlike
Altruistic Economics
AE18: The Imaginary Friends Test
v1.0
Recommended Pre-requisite: AE10: Keeping Score
A presentation by Dr. Robin Upton ( )
Available for download at
Attribution – NonCommercial - ShareAlike
Introduction to Imaginary Friends

2. Introduction to Imaginary Friends
Altruistic Economics is a decentralised system, so users have a lot of autonomy 
Artificial Construct 
Real Individual User
, such as
the chance to create Imaginary Friends:
Rewarding such Imaginary Friends would encourage deception.
F2F Network Growth

3. Each new member creates an online server and is linked in by friends.
F2F Network Growth
The Friend2Friend network grows organically, over real social relationships.  
Each new member creates an online server and is linked in by friends.     
The idea is, everyone has one online server.
However,like WWW, there is no centre, noone in charge, no list of members.
Sybil Attacks

4. The ‘Imaginary Friends’ Test
Sybil Attacks
‘Sybil’ was the first person diagnosed with so-called ‘Multiple Personality Disorder’.      
A Sybil Attack is an attempt to defraud an online system by using fake identities.
The ‘Imaginary Friends’ Test

5. The ‘Imaginary Friends’ Test
“Does it help to create ‘imaginary friends’?”
1. Imaginary Friends make no difference: 
PASS:  No Incentive to Cheat
2. Imaginary Friends are a disadvantage:  
3. Imaginary Friends are an advantage:  
FAIL:  Incentive to Cheat
Media Sharing

6. Media Sharing Aysha Birbal Chris
MEDIA SHARING is a project to network people who
review files and then benefit from one another’s opinions.
Aysha wants an opinion about the film ‘Chinese Whispers’…
Aysha
Birbal
I value your opinion…
I value your opinion…
“Chinese Whispers”
I know this film
Chris
How to quantify this process... ?
Basic Framework

7. Basic Framework Aysha Birbal Chris Assume:
Individuals make 2 sorts of evaluations:
1) ‘I value your opinion’ is quantified as V: <=V<=1
2) ‘I rate this File’ is quantified as R: <=R<=1
Individuals who don’t rate a file defer to their friends
Friends of friends’ opinions are valued multiplicatively
“Chinese Whispers”
Birbal
Aysha
I value your
opinion… 0.3
Chris
opinion… 0.4
I rate this file… 0.8
So Aysha has one recommendation:
Value=0.12 Rating=0.8
Combining Recommendations

8. Combining Recommendations
Ratings are averaged according to value, to give a single figure.
So, if Aysha has 4 recommendations:
Value=0.15 Rating=0.6
Value= Rating=0.5
Value=0.08 Rating=0.6
Value=0.12 Rating=0.8
Note the high value of the 2nd rating, which means it dominates the others.
0.15× × × ×0.8
Weighted average =
≈ 0.55
Applying The Test

9. What if Chris made Imaginary Friends to rate the file for him?
Applying The Test
What if Chris made Imaginary Friends to rate the file for him?
“Chinese Whispers”
MBogoN
Chris
MBogo2
Rating = R
I value your opinion… 1.0
MBogo1
Value=VB
I value your opinion… 1.0 …
Value=VB Rating=R … {
N separate ratings have
Overall value = NVB
A Problem

10. Chris could use his Imaginary Friends to dominate the other ratings.
A Problem
So, if Aysha has 4 recommendations:
Value= Rating=0.6
Value= Rating=0.5
Value= Rating=0.6
Value=NVB Rating=R
If N is big enough, no one else’s ratings count!
Chris could use his Imaginary Friends to dominate the other ratings.
Imaginary friends can increase an individuals’ impact,
so the algorithm fails the imaginary friends test.
A Modification

11. A Modification
To control the imaginary friends, we add a constraint to the model.
“Chinese Whispers”
MBogoN
Chris
MBogo2
Rating = R V1
MBogo1
Value=VB vN … v2
N friends give Chris N ratings,
with a value of ∑Vf. f
Let’s require ∑Vf=1 f
Summary of The ‘Imaginary Friends’ Test

12. Modified Algorithm Examined
With N>0 imaginary friends:
As an individual:
…} N such friends
MBogof
Rating = Rf
“Chinese Whispers”
Chris Vf VB VB
Chris
“Chinese Whispers”
Rating = R
Overall rating:
Value= VB∑Vf Rating=∑VfRf f
Single rating:
Value=VB Rating=R
Since ∑Vf=1, 1≥R,Rf≥0… f
imaginary friends confer no advantage.
So the modified algorithm passes the imaginary friends test.
Modified Algorithm Examined

13. Summary of The Imaginary Friends Test
Sybil Attacks are a feature of decentralised systems. 
Creating Imaginary Friends should not confer any advantage:
Applying the Imaginary Friends Test helps deduce algorithms suitable for decentralised systems.
Recommended Further Reading: AE19: Preventing Abuse