Kidney Exchange:
Where We’ve Been, and
Where We Can Go From Here
How is Economic Engineering different
from Economic Theory?
• Equivalently: How is practical market design
different from mechanism design?
• Practical market design isn’t eternal: we can
expect to do better as we learn more and as our needs change…
– Sometimes our needs change because of the way
Google data center
• So we shouldn’t expect even the best engineering
Brief history of kidney exchange
• Kidney exchange--early conceptual papers:
F. T. Rapaport (1986) "The case for a living emotionally related international kidney donor exchange registry," Transplantation Proceedings.
L. F. Ross, D. T. Rubin, M. Siegler, M. A. Josephson, J. R.
Thistlethwaite, Jr., and E. S. Woodle (1997) "Ethics of a
• The very first kidney exchanges were (as far as I know) carried out in S. Korea in the early 1990’s (where the percentage of blood types A and B are roughly equal)
• The first kidney exchange in the U.S. was carried
out at the Rhode Island Hospital in 2000
– Pre 2004: only 5 in the 14 transplant centers in
A classic economic problem: Coincidence of wants
(Money and the Mechanism of Exchange, Jevons 1876)
Chapter 1: "The first difficulty in barter is to find two persons whose disposable possessions mutually suit each other's wants. There may be many people wanting, and many possessing those things wanted; but to allow of an act of barter, there must be a double coincidence, which will rarely happen. ... the owner of a house may find it
unsuitable, and may have his eye upon another house exactly fitted to his needs. But even if the owner of this second house wishes to part with it at all, it is exceedingly unlikely that he will exactly reciprocate the feelings of the first owner, and wish to barter houses. Sellers and
purchasers can only be made to fit by the use of some
Section 301,National Organ Transplant Act
(NOTA),
42 U.S.C. 274e1984:
“it shall be unlawful for any person
to knowingly acquire, receive or otherwise
transfer any human organ for valuable
Charlie W. Norwood Living Organ
Donation Act
Public Law 110-144, 110th Congress, Dec. 21, 2007
• Section 301 of the National Organ Transplant
Act (42 U.S.C. 274e) is amended-- (1) in subsection (a), by adding at the end the following:
•
``The preceding sentence does not apply
Organization of kidney exchange on a large scale
• Roth, Sonmez and Unver (series of papers from
2004-2007):
– Cycles and chains (top trading cycles and chains…)
– 2-way exchange
– 2 and 3 way exchanges and non-directed donor
Compatibility graph: cycles
and
chains
Pair 1
Pair 2
Pair 3
Pair 4
Pair 6
Pair 7
Pair 5
Non-directed donor
Optimal choice of cycles and
chains
Pair 1
Pair 2
Pair 3
Pair 4
Pair 6
Pair 7
Pair 5
Non-directed donor
Modeling kidney exchange,
when it was new
• Players: patients, donors, surgeons
• Incentives: Need to make it safe for them to
reveal relevant medical information
• Blood type is the big determinant of compatibility
between donors and patients
• The pool of incompatible patient-donor pairs
looks like the general pool of patients with incompatible donors
• Efficient exchange can be achieved in large
Factors determining transplant opportunity
• Blood compatibility
So type O patients are at a disadvantage in finding compatible kidneys—they can only receive O kidneys.
And type O donors will be in short supply.
• Tissue type compatibility. Percentage reactive antibodies (PRA)
Low sensitivity patients (PRA < 79): vast majority of patients High sensitivity patients (80 < PRA < 100): about 10% of general
population, somewhat higher for those incompatible with a donor
Relevant information: patient antibodies to donor HLAs
O
A B
AB
18
A. Patient ABO Blood Type Frequency
O 48.14%
A 33.73%
B 14.28%
AB 3.85%
B. Patient Gender Frequency
Female 40.90%
Male 59.10%
C. Unrelated Living Donors Frequency
Spouse 48.97%
Other 51.03%
D. PRA Distribution Frequency
Low PRA 70.19%
Medium PRA 20.00%
Random Compatibility Graphs
n hospitals, each of a size c>0
D(n) - random compatibility graph:
1. n pairs/nodes are randomized –compatible pairs are disregarded 2. Edges (crossmatches) are randomized
Random graphs will allow us to ask two related questions:
What would efficient matches look like in an “ideal” large world?
What is the efficiency loss from requiring the outcome to be individually rational for hospitals?
(Large) Random Graphs
G(n,p) – n nodes and each two nodes have a non directed edge with probability p
Closely related model: G(n,M): n nodes and M edges—the M edges are distributed randomly between the nodes
Erdos-Renyi: For any p(n)¸(1+)(ln n)/n almost every large graph
G(n,p(n)) has a perfect matching, i.e. as n!1 the probability that a perfect matching exists converges to 1.
A natural case for kidneys is p(n) = p, a constant (maybe different for different kinds of patients), hence always above the threshold. “Giant connected component”
Similar lemma for a random bipartite graph G(n,n,p). Can extend also for r-partite graphs, directed graphs…
“Ideally” Efficient Allocations: if we were seeing all the patients in sufficiently large markets
21 Over-demanded (shaded) patient-donor pairs are all
matched.
B-A
B-AB A-AB
VA-B A-O B-O
AB-O
O-B O-A
A-B AB-B AB-A
O-AB O-O A-A B-B
AB-AB
Chains in an efficient large dense pool
It looks like a non-directed donor can increase the match size by at
most 3 22
Waiting list patient
Long chains have become a giant part
of contemporary kidney exchange
Can simultaneity be relaxed in
Non-directed donor chains?
• Cost-benefit analysis:
• “If something goes wrong in subsequent
transplants and the whole ND-chain cannot be completed, the worst outcome will be no
Chains initiated by
non-directed (altruistic) donors
Non-directed donation before kidney
exchange was introduced
Wait list
Non-directed
donor
Chains initiated by
non-directed (altruistic) donors
Non-directed donation before kidney exchange was introduced
Non-directed donation after kidney exchange was introduced
Wait list
Non-directed
donor
R1 D1
A chain in 2007…
3-way chain
March 22, 2007
BOSTON -- A rare six-way surgical transplant was a success in Boston.
There are only 6 people in this chain.
Simultaneity congestion: 3
transplants + 3 nephrectomies = 6 operating rooms, 6 surgical
Simultaneous cycles and
Non-simultaneous extended altruistic donor (NEAD) chains
On day 1 donor D2 gives a kidney to recipient R1, and on day 2 donor D1 is supposed to give a kidney to recipient R2…
D2
R2 R1
Conventional cycle: why always simultaneous?
Simultaneous cycles and
Non-simultaneous extended altruistic donor (NEAD) chains
Since NEAD chains can be non-simultaneous, they can be long D2
R2 R1
D1 D2
R2 R1 NDD Conventional cycle D1 Non-simultaneous chain
Roth, Alvin E., Tayfun Sönmez, M. Utku Ünver, Francis L. Delmonico, and Susan L. Saidman, “Utilizing List Exchange and Undirected Donation through “Chain”
The First NEAD Chain (Rees, APD)
Recipient PRA
* This recipient required desensitization to Blood Group (AHG Titer of 1/8).
# This recipient required desensitization to HLA DSA by T and B cell flow cytometry.
Chains are important for hard
to match pairs
• Why are chains essential? As kidney exchange
became common and transplant centers gained experience they began withholding their easy to match pairs and transplanting them internally.
• This means that the flow of new patients to kidney
exchange networks contain many who are hard to match
• So chains become important: many pairs with few
Why are hospitals doing internal matches?
And why is it costly?
Individual rationality and efficiency: an impossibility theorem (Ashlagi and Roth, forthcoming)
• For every k> 3, there exists a compatibility
graph such that no k-maximum allocation which is also individually rational matches more than 1/(1) of the number of nodes matched by a k-efficient allocation. Furthermore in every
Proof (for k=3)
a3
a2
c
d a1
Could be fixed…
• …with a ‘frequent flier’ program of incentives for hospitals
Theorem: If every hospital size is regular and bounded than in almost every large graph the efficiency loss
from a maximum individually rational allocation is at most (1+)AB-Om + o(m) for any >0 (less than 1.5%).
So the worst-case impossibility results don’t look at all like what we could expect to achieve in large kidney
exchange pools (if individually rational mechanisms are adopted).
But we haven’t (yet) solved the political problems
associated with guaranteeing hospitals an individually rational allocation
2.09% 2.56%
4.18%
5.81%
14.38%
95-96 96-97 97-98 98-99 99-100
The APD cares for many very
highly sensitized patients
High PRA patients had a median waiting time of >13 years for a deceased donor kidney
PRA (panel reactive antibody) level
Compatible with fewer than 1% of kidneys. Looking for a needle in a haystack.
Graph induced by pairs with A patients and A donors. 38 pairs (30 high PRA). Dashed edges are parts of cycles.
So we need to model sparse graphs…
• We’ll consider random graphs with two kinds of nodes
(patient-donor pairs): Low sensitized and high sensitized
• L nodes will have a constant probability of an incoming edge
(compatible kidney). They will be the overdemanded pairs.
• H nodes will have a probability that decreases with the size of
the graph (e.g. in a simple case we’ll keep the number of compatible kidneys constant, pH = c/n)
• In the H subgraph, we’ll observe trees but almost no short
cycles
• A non-directed donor can be modeled as a donor with a
patient to whom anyone can donate—this allows non-directed donor chains to be analyzed as cycles
• (We also consider the effect of different assumptions about
Cycles and paths in random dense-sparse graphs
• n nodes. Each node is Low w.p. and High w.p. 1-
• incoming edges to L are drawn w.p. •incoming edges to H are drawn w.p.
L
Cycles and paths in random sparse (sub)graphs (v=0, only highly sensitized patients)
H
Theorem.
(a) The number of cycles of length O(1) is O(1). [the number of cycles of constant length is roughly constant]
(b) But when pH is a large constant there is cycle with length O(n) “Proof” (a):
44
Cycles and paths in random sparse graphs (v=0)
H
Theorem.
(a) The number of cycles of length O(1) is O(1).
(b) But when pH is a large constant there is path with length O(n)
Since cycles need to be short (as they need to be conducted
Case v>0 (some low sensitized, easy to match patients. Why increasing cycle size helps
L
H
Theorem. Let Ck be the largest number of transplants achievable with cycles · k. Let Dk be the largest number of transplants achievable with
cycles · k plus one non-directed donor. Then for every constant k there exists >0
Case v>0. Why increasing cycle size helps
Increasing cycle lengths significantly increases transplants. Highly sensitized patients are the principal beneficiaries.
Low sensitized pairs of all blood types are overdemanded: it’s easy to start a cycle from L to H since there are many H, and easy to end it back in L since most blood type
Case v>0. Why increasing cycle size helps
Increasing cycle lengths significantly increases transplants. Highly sensitized patients are the principal beneficiaries.
Low sensitized pairs of all blood types are overdemanded: it’s easy to start a cycle from L to H since there are many H, and easy to end it back in L since most blood type
The view from Johns Hopkins
Hospital
• Gentry SE, Montgomery RA, Swihart BJ, Segev
DL. The roles of dominos and nonsimultaneous chains in kidney paired donation. Am J
Transplant 2009;9(6):1330- 1336
• Conclusions: “NEAD chains did not yield more
NDD R1 D1 Wait List R2 D2 NDD R1 D1 R2 D2 R3 D3
A modeling mistake
• Model restricted length of non-simultaneous chains
• Correction: Ashlagi, Itai, Duncan S. Gilchrist, Alvin E.
Roth, and Michael A. Rees, ''Nonsimultaneous Chains and Dominos in Kidney Paired Donation -- Revisited,'' American Journal of Transplantation, 11, 5, May 2011, 984-994.
• “As this finding contrasts with the experience of several groups involved in kidney-paired donation, we
performed simulations that allowed for longer chain segments and used actual patient data from the
A further exchange
• Gentry SE, Segev DL. The honeymoon phase
and studies of nonsimultaneous chains in kidney paired donation. Am J Transplant
• Conclusion: “We maintain that NEAD chains
do not, in the long run, create more
Resolution
• Ashlagi, Itai, Duncan S. Gilchrist, Alvin E. Roth, and Michael A. Rees, "NEAD Chains in Transplantation," American
Journal of Transplantation, December 2011, 11:2780-2781. • “Gentry and Segev speculate that the results reported in
Ashlagi et al, that nonsimultaneous extended altruistic donor (NEAD) chains produce more transplants than
domino-paired donation (DPD), would be reversed if the computation were conducted for more periods. We carry out the computation and show that, contrary to their conjecture, nonsimultaneous chains continue to allow more transplants than simultaneous chains, even over a longer time horizon. Furthermore, more highly sensitized patients are transplanted by allowing chains to continue with bridge donors rather than automatically ending with donations to patients on the deceased donor waiting
…In a groundbreaking program at Johns Hopkins
Hospital that is as much about nationwide
networking as it is medical innovation, kidney transplants are being arranged not through isolated pairings of patient and donor, but
through longer and longer chains of individuals
who don’t even know each other.
Recall: Modeling kidney exchange,
when it was new
• Players: patients, donors, surgeons
• Incentives: Need to make it safe for them to
reveal relevant medical information
• Blood type is the big determinant of compatibility
between donors and patients
• The pool of incompatible patient-donor pairs
looks like the general pool of patients with incompatible donors
• Efficient exchange can be achieved in large
Modeling kidney exchange,
today
• Players: patients, donors, surgeons
• And transplant centers, and kidney exchange
networks
• Incentives: Need to make it safe to reveal
relevant medical information, and to enroll easy to match patient donor pairs, and
Modeling kidney exchange,
today
• Players: patients, donors, surgeons
• And transplant centers, and kidney exchange
networks
• Incentives: Need to make it safe to reveal relevant medical information, and to enroll easy to match patient donor pairs, and collaborate to enlarge the pool of pairs
• Blood type is Antibodies are the big determinant of compatibility between donors and patients
• The pool of incompatible patient-donor pairs looks like much more highly sensitized than the general pool of patients with incompatible donors
Modeling kidney exchange,
today
• Efficient exchange can be achieved in large
Modeling kidney exchange,
today
• Efficient exchange can be achieved in large
enough markets (but not infinitely large) with exchanges and chains of small sizes
• But markets of the size and composition that we
are currently seeing require long chains, which not only increase the number of transplants but often provide the only way to transplant very highly sensitized patients.
Varieties of evidence
• Theory
• Simulations
• Resampling of clinical data
– Itai Ashlagi and I have been looking at the history of patient/donor enrolment in some of the biggest
kidney exchanges, and simulating different policies on those populations
• Performance of different kidney exchange
networks
New sets of players
• Kidney Exchange Institutions
– NEPKE (2004-2011) – APD (2005-)
– UNOS national pilot program (2010-) – NKR (2007-)
– Others…e.g. Mayo Clinic,…
– Single-center kidney exchange programs
• San Antonio, Northwestern
– Big transplant centers that both participate in networks and do internal exchanges
• Centers sometimes withhold easy to match pairs, so the
pairs submitted to exchange networks are hard to match…
Kidney exchange institutions
single center, multi-center, national pilot (A convenience sample of kidney exchange
programs with which Itai Ashlagi and I are working)
• Methodist San Antonio-single center (Adam
Bingaman et al.)
• Alliance for Paired Donation (Mike Rees et al.) • National Kidney Registry (Garet Hil et al.)
• UNOS Pilot program (USA et al….Tuomas
Quick summary: the ability to do long
chains is important
• NKR: 615 Transplants 2008-12 (139 NDD chains, ~90%
of transplants via chains)
– 25% cPRA >80%
• Methodist San Antonio KPD program (2008-): 210
transplants, 6 NDD chains (and many compatible pairs) • Alliance for Paired Donation: 178 transplants (24 NDD
chains, 76% of transplants via chains)
– 21% PRA>80%
• UNOS/OPTN KPDPP 2010-12: 27 transplants (42 NDDs)
– …the OPTN Board of Directors voted in Nov 2012 to
include bridge donors in the OPTN program.(Chains had been capped for a while at length 4) [In 2013 there have already been an additional 17 transplants as of April 30.]
NKR: 615 Transplants 2008-12 (139 NDD chains)
21
62
131
175
226
Methodist San Antonio KPD program
(includes compatible pairs)
• 210 KPD transplants done (this slide 2013)
– Thirty-Three 2-way exchanges
– Twenty-three 3-way exchanges
– Two 6-recipient exchanges
– One 5-recipient chain
– One 6-recipient chain
– One 8-recipient chain
– One 9-recipient chain
– One 12-recipient chain
– One 23-recipient chain
Initiated in 2008
Alliance for Paired Donation
• # of transplants: 178
• # via chains: 135 (75.8%)
Organ Procurement and Transplantation Network (OPTN) Kidney Paired Donation Pilot Program
(KPDPP): Review of Current Results (2010-12)
R. Leishman, R. Formica, K. Andreoni, J. Friedewald, E. Sleeman, C. Monstello, D. Stewart, T. Sandholm
• Background: On Oct 27, 2010, the OPTN KPDPP ran its first of 40 match runs. 128 transplant centers
representing all 11 regions have joined, with 79 centers having entered at least one pair. …
• Methods: Candidate and donor data were submitted from Oct 2010 – Nov 2012
• Results: A total of 610 candidates and 673 donors
(including 42 non-directed donors) have been entered.
A total of 27 candidates have been transplanted. 444
of 478 match offers (93%) have been declined.
• …the OPTN Board of Directors voted in Nov 2012 to
OPTN KPD Pilot Program: Number of KPD
Transplants by Year
2 15 10 17 0 2 4 6 8 10 12 14 16 18
2010 2011 2012 2013
2010 2011 2012 2013 Through May,2013
Growth of kidney exchange
in the US
Kidney exchange transplants per year
2 4 6 19 34 27 74 111
228 281
430 446
528 590
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Another problem: patient-donor pools
are fragmented
Benefits of merging patient-donor
pools: over 3 years of data (with
duplicates removed)
NKR +
APD + SA SA + APD NKR + APD NKR + SA
All matches 17% (5%) 11% (1.5%) 15% (4%) 8% (2.5%) PRA >= 80
matches 38% (10%) 21% (5%) 25% (4%) 17% (25) PRA >= 95 63% (16%) 25% (6%) 45% (13%) 22% (4%) PRA >= 99 73% (19%) 35% (7%) 63% (10%) 16.6% (5%)
3 years of data from each program: match each week, including
failures…separately about 8 pairs each of nkr and apd per week and 4 for sa , resampling arrival time in actual clinical data 15% more from full match (still one week, so more pairs) 3% run each program separately, but every 2
Collaboration between SA, NKR and
APD -
280 380 480 580 680 780 880
Separate pools Monthly collaboration Full collaboration
All
Collaboration between SA, NKR and
APD - Hardest to match patients
0 20 40 60 80 100 120 140
Separate pools Monthly
collaboration Full collaboration
97+ PRA 99+ PRA
But innovation has come from having
multiple kidney exchange programs
• APD
– Non-simultaneous chains – International exchange
– Finance: Standard Acquisition Fee
• San Antonio
– Compatible pairs
– Novel cross matching
• NKR
– Immediately re-optimizing whole match after a rejection – Prioritizing via both patient and donor difficulty in matching – Recruiting NDD’s
• Various centers
– Integrating desensitization into kidney exchange
So…
• I think it would be premature to move to a single
kidney exchange network now
– (despite the huge logistics advantages offered by UNOS in theory, but not yet in practice…)
• But the time may be ripe to foster cooperation
and coordination among kidney exchange networks
– Partial pooling, among networks’ unmatched pairs, will create gains in numbers of transplants while still
More general issues: economist view
• Transplant center business models
• The number of transplant centers has grown over
time (as transplant fellows were trained…)
– There are advantages to big, high volume centers, and different advantages to local/regional care
– Analogously, kidney exchange may lead to different distribution of patients than desensitization:
Transplant policies have implications for
transplant centers and physicians…these need to be better discussed.
• E.g.
– How will we finance kidney exchange among multiple centers?
– Why are transplant centers withholding easy-to-match pairs?
– partial cooperation between kidney exchange networks (rather than a single network)
– regional deceased donor lists
• Bottom line: medical care, and the organizations
Kidney exchange outside the U.S.
• December 19, 2013 Kidney exchange in Vienna
• August 19, 2013 Ten kidney exchange transplants on World Kidney Day in
Ahmedabad, India
• July 28, 2013 First Kidney Exchange in Portugal: • July 23, 2013 Kidney exchange chain in India
• June 6, 2013 Kidney exchange between Jewish and Arab families in Israel • December 26, 2012 Kidney exchange in Canada
• December 1, 2012 Kidney exchange in India
• June 1, 2012 Mike Rees and Greece: an intercontinental kidney exchange • March 27, 2012 Kidney exchange in Britain
• February 5, 2012 Kidney exchange in Australia, 2011 • April 29, 2011 First kidney exchange in Spain
• December 8, 2010 National kidney exchange in Canada • August 3, 2010 Kidney Exchange in South Korea
• March 9, 2010 Kidney exchange news from Britain (1st 3-way there)
• January 27, 2010 The Australian paired Kidney eXchange (AKX) goes live • June 25, 2009 Kidney exchange in Canada (1st exchange there)
Now we need to think about ways to
make and keep the market thick:
Incentives for transplant centers to contribute easy to match pairs and
Kidney failure is a >$50 Billion industry
in the U.S.
• At > $8 Billion it’s the single biggest program
in Medicare
• So there are lots of interests involved, lots of
institutions and ways of doing things
• Practical market design involves finding ways
to work with and around all of these to get things done
– We have to guard against viewing markets too
Behavioral issues: Motivation of donors?
• Standard live donors can have standard motivations:
love of spouse, etc.
• Nondirected live donors are some flavor of altruist. • Bridge donors?
– A deal’s a deal? – More complicated?
• Also need to think about how to increase deceased
donation:
– Kessler, Judd B. and Alvin E. Roth, “Organ Allocation Policy
Why do we have laws against simply
buying and selling kidneys?
• I sure don’t know the answer to this one, but I
think it’s a subject that social scientists need to study…
Repugnance
• Let’s call a transaction repugnant if some
Repugnant transactions
• some historically important repugnances
– Sex (outside of marriage, incest, homosexuality,
pornography, prostitution…) • Same-sex marriage
– Servitude: Slavery and serfdom and indentured
servitude
– Worship (Inquisitions, expulsions, heresy,
religious wars, blasphemy)
– Interest on loans (was repugnant, no longer so much)
First Gay Marriages Take Place in
England and Wales
Changes over time in both directions
• There are markets that were once repugnant
but no longer are.
• And there are markets that are repugnant
Lending money for interest
• Once widely repugnant, now not (with the
important exception of Islamic law).
• Albert Hirschman paraphrases Max Weber’s
question in “The Spirit of Capitalism”:
– “How did commercial, banking, and similar money-making pursuits become honorable at
Credit. Man’s Confidence in Man. “Commercial credit is the creation of modern times and belongs in its highest perfection only to the most enlightened and best governed nations. Credit is the vital air of the system of modern commerce. It has done more — a thousand times more —
Why can’t you eat horse or dog meat in a
restaurant in California?
1. Short answer: It’s against the law.
• California Penal Code Section 598 states in part “…horsemeat may not be offered for sale for human consumption.”
2. Longer answer: many Californians find it repugnant that anyone should eat a horse
Ontario
Dwarf Tossing Ban Act, 2003
• Bill 97 2003 An Act to ban dwarf tossing
• Her Majesty, by and with the advice and consent of the
Legislative Assembly of the Province of Ontario, enacts as follows:
• Dwarf tossing banned
• 1. (1) No person shall organize a dwarf tossing event or
engage in dwarf tossing.
• Offence
• (2) A person who contravenes subsection (1) is guilty of an offence and on
conviction is liable to a fine of not more than $5,000 or to imprisonment for a term of not more than six months, or to both.
• Commencement
• 2. This Act comes into force on the day it receives Royal Assent. • Short title
Dwarf tossing
U.N. Human Rights Committee backs 'dwarf-tossing' ban (2002)
Manuel Wackenheim began his fight in 1995 after dwarf tossing bans were upheld in France.
• The U.N. case report quotes Wackenheim to the effect
that “there is no work for dwarves in France and that his job does not constitute an affront to human dignity since dignity consists in having a job.”
• The UN committee found for France, saying "the ban
on dwarf-tossing was not abusive but necessary in
order to protect public order, including considerations
Repugnance can be hard to predict
• Why is dwarf tossing widely regarded as
repugnant?
• It’s not just the small size of the dwarfs
102
Wife Carrying—Not Repugnant?
Money and repugnance
• Often x+$ is repugnant, even when x alone
isn’t.
– E.g. interest on loans,
Sometimes it’s not the presence of
money, but the
amount
•
Price gouging
:– High prices can be repugnant
– Uber is meeting resistance to “surge pricing”
– Common headlines after hurricanes, etc:
105
“We didn’t have time to pick up a bottle of wine, but this is what we would have spent.”
Money and repugnance
• There seem to be three principal lines of
argument about how adding money makes a non-repugnant transaction repugnant:
– Objectification
Transactions between consenting adults
• Test yourself for repugnance: are you willing
to contemplate the investigation (and perhaps eventual adoption) of carefully regulated sales of live: