Robert B. Loring
5911 Springfield Drive
Bethesda, MD 20816

								September 19, 1990

Professor John R. Chamberlin
440 Lorch Hall, Institute of Public Policy Studies
611 Tappan Street
University of Michigan,  Main Campus
Ann Arbor,  Michigan  48109-1220

Professor Chamberlin,

	Thanks for your quick reply to my paper.  I’m happy to hear that you think my new system is an improvement over Hare’s STV.  The references you included are indeed helpful and I shall use them.

	Another reply to the same paper stated  “I think your advocacy of C-AV will hinge on the relative merits of the completion procedure when Condorcet fails.  Thus one needs to compare C-AV primarily with Black, max-min, etc.  General results on manipulability don’t help much here;  what is crucial is what happens in the unusual conditions when there is no Condorcet winner.  Your examples are good (even one counter-example!), but can you treat it more systematically?  If I get time, I will try a simulation of social-utility efficiency for C-AV.”  

	I’m not sure, but it appears he may have missed the point that, given the manipulation attempts possible or likely in real electorates, Condorcet can fail often — as shown by your analyses of manipulability in the APA and simulated electorates.  Given strategic voting, the new system may have the highest efficiencies for electing the sincere Condorcet and utility maximizing winners.   

	I have written a fairly strong proof of that assertion.  But my proof is based mainly on logical extrapolations from previous research.  I have no experience at programing simulations.  Is a simulation to determine the efficiencies of several voting systems, given realistic ballots and various degrees of manipulation, the next logical step in your work?  I’d like very much to see the results of that simulation for the voting rules which seem most resistant to manipulation.  They may include max-min, mine, Dodgson’s, Kemeny’s, and your 1985 completion rule which built on Kemeny’s.  Plurality, Borda, Hare, and approval voting might be worth including for comparison.  I hope my efforts can interest you in this research as your work inspired me.

	Thanks again for your help, I look forward to reading more of your work.

	Sincerely,

	Robert B. Loring

P.S. minor notes on page two.

	Some of the Australians I’ve read have referred to single-winner Hare as the “alternative vote” system for many years.  That seems a short, clear description.  But you call it STV and Samuel Merrill says that some readers may mistake the “AV”  in “C-AV” for approval voting.  So I shall change the acronyms used in the paper to M-STV and    C-STV.  

	The journal condensation of the essay will conclude along these lines:

Summary and Recommendations

	C-STV’s winners beat M-STV’s whenever the two rules elect different winners.  In the absence of voting cycles, at least as many voters support C-STV’s winners as those elected by any other voting rule.  

	When both C-STV and M-STV are manipulable, C-STV often is harder to manipulate because a larger number of voters must coordinate their strategies.  C-STV is more often impossible to manipulate than any other voting system except M-STV.  M-STV resists better only when it inherently errs by failing to elect the one candidate whom a majority of voters support over every other one.  

	With 100% Condorcet efficiency and strong resistance to manipulation, C-STV is the most reliable way to elect the candidate with the broadest support among voters.  By electing only such widely supported candidates, C-STV would create a poor legislature, one which would not represent the voices of minorities.  But this new system’s characteristics make it one of the best for electing a president.  

Frequency in general elections
Effects on C-STV relative to other voting systems

xx 1) No cycle & no manipulation:   
Frequency 2	This probably occurs often.  
Effects 	C-STV performs very well.
¶ OK  
	At least as many voters support C-STV’s winners as those elected by any other voting rule.  (But its utility value might be lower than Borda’s — Chamberlin’s “Nearness” seems to disagree with the utility efficiencies reported by Merrill and Bordley.  Ask Chamberlin about this.)

√x 2) A natural cycle and no manipulation:  
Frequency 4	This rarely happens.  
Effects 	C-STV performs poorly.
¶ OK  
	C-STV equals M-STV.  Borda, Black, Kemeny, and many other rules result in higher utility efficiencies than Hare under most conditions.  This probably is as true in elections with voting cycles as in other elections.  Those systems’ winners have larger victories and smaller losses than C-STV’s winners do.  So in that sense they have broader support.  

x√ 3) No natural cycle and various attempts at manipulation:
	One-sided manipulation in closely-contested multi-candidate elections can always create a cycle and can change the winners under all voting systems (except Hare).  But that is not true under less one-sided conditions.  Under these conditions all rules allow the sincere winner’s supporters to counter-manipulate.  Such multi-party manipulations create a risk of electing darkhorse candidates.  Depending on the manipulations which occur, voting systems of all kinds will elect various ratios of sincere winners, runners-up and darkhorse candidates.  So the simulated Condorcet and utility efficiencies of all rules will depend on the manipulations we assume.
Frequency 1	We do not know the frequency of different manipulation patterns.  
M-STV is the best system for discouraging these attempts because of the information needed to predict STV’s sincere winner, plan strategies, and persuade voters, all added to the rare manipulability of STV.
Effects: 	We can simulate the effects of manipulation patterns.  If many different patternslead to the same ranking of voting systems on Condorcet and utility efficiencies, then we may say some systems are better than others.  
	When manipulation does succeed under C-STV it must create a voting cycle.  Then the manipulated winner is most often the STV winner.  If  STV wins are distributed evenly it produces low Condorcet and utility efficiencies.  But if STV’s Condorcet efficiency is high then candidates and voters rarely have an incentive to create a cycle by punishing the leader.   The latter is supported by research using actual ballots and polls: Chamberlin 198? page_?, Tideman 1980? page_?;  but not by simulated elections: Merrill 1988, page__
	Even if M-STV’s efficiencies are high, C-STV is still an improvement.  Its efficiencies will always be as high or higher due to elections where M-STV would not elect the Condorcet winner and voters do not succeed in creating a voting cycle.
	When a manipulation succeeds under the STV eliminations, after a cycle, is the winner often the utility maximizer?  She generally has the most first-place votes to use in squeezing another candidate.  
	If cycles result more often from a manipulation than from sincere ballots, then we may follow Chamberlin’s 1985 suggestion to...     
	When a manipulation succeeds under other systems the winner is _(?).  Just making a cycle doesn’t help any candidate under Black because that leads to the Borda rule which still elects the utility maximizer — who is probably the sincere Condorcet winner.  But Borda’s rule is easy to manipulate by punishing the leader.  (— which you do to create a voting cycle.)

√√ 4) A natural cycle & various attempts at manipulation (or counter-manipulation):
Frequency: 	This rarely happens.  
Effects:	C-STV performs about as poorly as in two above? 
¶ Dense  
	C-STV equals M-STV.  They usually cannot be manipulated.  
Their utility efficiency probably varies widely in simulated sincere elections with voting cycles..  Their utility efficiency is _(?) in manipulated elections with voting cycles.  (Under all rules a low utility candidate sometimes can manipulate to take an election from the utility maximizer.  But I suspect that often under STV, the utility maximizer with many first-place votes can manipulate to win — if the information needed can be gathered and communicated.  (This is in part due to C-STV’s low utility efficiency and in part because the utility maximizer has a relatively high share of the first-place votes needed to manipulate STV.) 

	I think 1 and 3 are more common than 2 and 4.  I think C-STV will equal the best systems in condition one.  I think C-STV will be the best system under condition three. 

Prose
	When manipulation is at low levels and frequencies then Borda will have a slightly higher utility efficiency than C-STV.  At what levels * frequencies of manipulation will C-STV surpass Borda?  That probably happens at very low levels if the manipulation is one sided or asymmetric. (by one party not countered)  It is not trivial to estimate or deduce which system fails to elect the sincere Condorcet winner most frequently or at the lowest levels of manipulation when the Condorcet winners’ party counter manipulates or when third parties manipulate their ballots. 
	At the very least C-STV sets a higher standard than Hare for Condorcet and utility efficiencies under conditions of manipulation.  And higher than any other voting system under one-way manipulation.  Probably higher under asymmetric manipulation.