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Re: Application of Range-Approval Hybrid to Shift Bidding

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  • brokenladdercalendar
    the current system needs to use vickrey, because nurses have an incentive to overbid, in the scheme you describe.
    Message 1 of 21 , Sep 1, 2009
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      the current system needs to use vickrey, because nurses have an incentive to overbid, in the scheme you describe.
    • jclawrence2
      ... What s vickrey?
      Message 2 of 21 , Sep 1, 2009
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        --- In RangeVoting@yahoogroups.com, "brokenladdercalendar" <thebrokenladder@...> wrote:
        >
        > the current system needs to use vickrey, because nurses have an incentive to overbid, in the scheme you describe.
        >

        What's vickrey?
      • Raph Frank
        ... The idea is to minimise the cost to society. However, it should increase the utlity for the nurses anyway. That is what is great about allowing free
        Message 3 of 21 , Sep 1, 2009
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          On Tue, Sep 1, 2009 at 1:03 AM, jclawrence2<j.c.lawrence@...> wrote:
          > However, shift bidding does not maximize individual or social utility
          > among the nurses.

          The idea is to minimise the cost to society. However, it should
          increase the utlity for the nurses anyway. That is what is great
          about allowing free markets to operate. Both sides benefit.

          The natural effect is to assign nurses who don't mind the night shift
          to work mostly night shifts. They win (as they get more money), the
          other nurses win (as they don't have to work nights as much) and the
          hospital wins as it pays less (and probably has happier staff).

          How do the current auctions work? Does the system increase the pay
          until only 1 nurse is willing to work for that hour?

          > Visualize a system in which the nurses rate each shift
          > and hourly pay rate according to its utility to them and the hospital
          > tries to maximize social utility among the nurses.

          I think you can reasonably assume that the utility value of money is
          linear for the nurses.

          I think the effort/negative utility for the nurse of each hour worked
          wouldn't be linear though.

          A 20 hour shift is more than double as bad as a 10 hour shift.

          I think the cost of a shift is probably something like

          (fixed cost) + (effort)*(hours worked)^(fatigure coefficient)

          The fixed cost is the cost of driving to and from work etc. A one
          hour shift would need to pay much more than half of what a 2 hour
          shift does.

          Similarly, longer shifts would need to pay more due to fatigue etc.

          The nurse could her preferred shift length (which balances fatigue and
          the fixed costs). For shifts of other lengths, she could indicate the
          surcharge. For example, a nurse who wants a 9 hour shift might be
          willing to work an 8 hour shift from +15% per hour from the stated
          amounts.

          > This would seem to me to be a great improvement over shift bidding for
          > the nurses and also for the hospital in that it would set an overall
          > budget whereas with shift bidding the hospital's budget would be
          > variable and subject to manipulation because the hospital would have to
          > make sure that all shifts were adequately covered regardless of labor
          > costs.

          I would also be concerned with union-like effects where all the nurses
          agree to a lower limit for their bids.

          Also, I don't agree that keeping nurses wages higher is a good thing.
          If they are willing to work for less, I don't see why that shouldn't
          be supported.

          Finally, there is no real system where it is optimal to be honest and
          also gets best utility. CTT does it in theory but is unlikely to do
          it in practice.

          I am not really sure what you are actually proposing. There comes a
          point where you are collecting more information than it is worth
          collecting.
        • brokenladdercalendar
          google vickrey auction . the deal is, right now a nurse might honestly bid 30 bucks an hour for some shift. if it s really worth that much to her, then she
          Message 4 of 21 , Sep 1, 2009
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            google "vickrey auction".

            the deal is, right now a nurse might honestly bid 30 bucks an hour for some shift. if it's really worth that much to her, then she "breaks even".

            but, if she bids insincerely higher, like 35 bucks an hour, then the either

            a) doesn't get it, in which she still breaks even (does zero work, and makes zero money)
            b) still gets it, for more than she thought it was worth, meaning there's a small chance she _profits_.

            you want to take away that incentive for the nurse to overbid, so you can use a vickrey auction. just make sure the lowest-bidding nurse wins, but gets paid what the second-lowest-bidding nurse bid. thus no incentive to overbid.

            --- In RangeVoting@yahoogroups.com, "jclawrence2" <j.c.lawrence@...> wrote:
            >
            > --- In RangeVoting@yahoogroups.com, "brokenladdercalendar" <thebrokenladder@> wrote:
            > >
            > > the current system needs to use vickrey, because nurses have an incentive to overbid, in the scheme you describe.
            > >
            >
            > What's vickrey?
            >
          • warren_d_smith31
            I did not understand this nurse shift bidding stuff. The point of the bidding was to benefit the hospital and screw the nurses by giving nurses minimum money
            Message 5 of 21 , Sep 1, 2009
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              I did not understand this nurse shift bidding stuff.

              The point of the bidding was to benefit the hospital and screw the nurses by giving
              nurses minimum money for the work.

              And now you are saying we should do some kind of utility maximization to
              benefit the nurses (max utility) and therefore screw the hospital. For example, pay
              the nurses max money, not min money (if the nurses claim utility=money).

              Which is the goal?
            • jclawrence2
              I think as presently used the shifts are fixed 8 hours. So the only choice is which of 3 eight hour shifts the nurse wants to bid on for any particular day. It
              Message 6 of 21 , Sep 1, 2009
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                I think as presently used the shifts are fixed 8 hours. So the only choice is which of 3 eight hour shifts the nurse wants to bid on for any particular day. It works out that the less desirable shifts are bid higher so the nurse makes more money for those. So she can work less total hours per week and still make as much as someone working more hours on the more desirable shifts.

                The hospital makes out because, if there are no nurses signing up for the less desirable shifts, they have to hire them from an agency and pay them a lot more including the agency's fee. They would rather pay their own nurses more to work those shifts because they are more familiar with the particular hospital. So it does keep labor costs down while allowing nurses to have flexible hours and shifts and to make more than the going rate if they so choose.

                As you point out, union effects could screw up the system as well as an overabundance of nurses. The system was designed I think for the situation of a relative nursing shortage.

                What I am proposing is that each nurse assign a utility to each shift/wage combination and then the system would seek to assign shifts in such a way as to maximize utility subject to some constraints like minimum and maximum hourly pay and overall budget. To simplify, and, for example, nurse A could assign the utility .1 to shift 1 at a $20. rate, .5 to shift 1 at a $30. rate and .8 to shift 1 at a $45. rate and so on with utilities varying from 0 to 1. Too high bids would tend to be eliminated due to the overall budget constraint and too low bids would tend to be eliminated due to the goal of maximizing social utility.


                --- In RangeVoting@yahoogroups.com, Raph Frank <raphfrk@...> wrote:
                >
                > On Tue, Sep 1, 2009 at 1:03 AM, jclawrence2<j.c.lawrence@...> wrote:
                > > However, shift bidding does not maximize individual or social utility
                > > among the nurses.
                >
                > The idea is to minimise the cost to society. However, it should
                > increase the utlity for the nurses anyway. That is what is great
                > about allowing free markets to operate. Both sides benefit.
                >
                > The natural effect is to assign nurses who don't mind the night shift
                > to work mostly night shifts. They win (as they get more money), the
                > other nurses win (as they don't have to work nights as much) and the
                > hospital wins as it pays less (and probably has happier staff).
                >
                > How do the current auctions work? Does the system increase the pay
                > until only 1 nurse is willing to work for that hour?
                >
                > > Visualize a system in which the nurses rate each shift
                > > and hourly pay rate according to its utility to them and the hospital
                > > tries to maximize social utility among the nurses.
                >
                > I think you can reasonably assume that the utility value of money is
                > linear for the nurses.
                >
                > I think the effort/negative utility for the nurse of each hour worked
                > wouldn't be linear though.
                >
                > A 20 hour shift is more than double as bad as a 10 hour shift.
                >
                > I think the cost of a shift is probably something like
                >
                > (fixed cost) + (effort)*(hours worked)^(fatigure coefficient)
                >
                > The fixed cost is the cost of driving to and from work etc. A one
                > hour shift would need to pay much more than half of what a 2 hour
                > shift does.
                >
                > Similarly, longer shifts would need to pay more due to fatigue etc.
                >
                > The nurse could her preferred shift length (which balances fatigue and
                > the fixed costs). For shifts of other lengths, she could indicate the
                > surcharge. For example, a nurse who wants a 9 hour shift might be
                > willing to work an 8 hour shift from +15% per hour from the stated
                > amounts.
                >
                > > This would seem to me to be a great improvement over shift bidding for
                > > the nurses and also for the hospital in that it would set an overall
                > > budget whereas with shift bidding the hospital's budget would be
                > > variable and subject to manipulation because the hospital would have to
                > > make sure that all shifts were adequately covered regardless of labor
                > > costs.
                >
                > I would also be concerned with union-like effects where all the nurses
                > agree to a lower limit for their bids.
                >
                > Also, I don't agree that keeping nurses wages higher is a good thing.
                > If they are willing to work for less, I don't see why that shouldn't
                > be supported.
                >
                > Finally, there is no real system where it is optimal to be honest and
                > also gets best utility. CTT does it in theory but is unlikely to do
                > it in practice.
                >
                > I am not really sure what you are actually proposing. There comes a
                > point where you are collecting more information than it is worth
                > collecting.
                >
              • jclawrence2
                Actually the nurses tended to make more under the bidding system and the hospital also reduced labor costs since there was a relative nursing shortage. For
                Message 7 of 21 , Sep 1, 2009
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                  Actually the nurses tended to make more under the bidding system and the hospital also reduced labor costs since there was a relative nursing shortage. For unfilled shifts the hospital had to go to a temp agency and pay more for less qualified nurses. Under the bidding system, the regular nurses tended to fill all the shifts and made more money while reducing overall labor costs and also providing higher quality care since the hospital ended up using fewer agency nurses.

                  What I am proposing is a system that would allow each nurse to assign utilities to each wage/shift combination and then the system would seek to maximize social utility subject to an overall budget constraint. The overall budget might be something negotiated between the nurses' union and the hospital management. Also constrained might be max and min hourly rates. For example, each nurse might assign 3 utilities to each shift: for shift 1 they might be .1 for a $20. hourly wage, .5 for a $30. hourly wage and .8 for a $45. hourly wage. Utilities vary between 0 and 1.

                  Higher wage amounts would tend to be eliminated due to the overall budgetary constraint and lower wage amounts would tend to be eliminated due to the goal of maximizing utility. The hospital would benefit because it would have fixed labor costs known in advance, and the nurses would benefit because their individual utilities would tend to be maximized and they would have a lot of flexibility.

                  --- In RangeVoting@yahoogroups.com, "warren_d_smith31" <wds@...> wrote:
                  >
                  > I did not understand this nurse shift bidding stuff.
                  >
                  > The point of the bidding was to benefit the hospital and screw the nurses by giving
                  > nurses minimum money for the work.
                  >
                  > And now you are saying we should do some kind of utility maximization to
                  > benefit the nurses (max utility) and therefore screw the hospital. For example, pay
                  > the nurses max money, not min money (if the nurses claim utility=money).
                  >
                  > Which is the goal?
                  >
                • jclawrence2
                  ... I don t think so because there is effectively a maximum bid. If a regular nurse bids too high the hospital will use a temp agency nurse at a fixed price.
                  Message 8 of 21 , Sep 1, 2009
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                    --- In RangeVoting@yahoogroups.com, "brokenladdercalendar" <thebrokenladder@...> wrote:
                    >
                    > the current system needs to use vickrey, because nurses have an incentive to overbid, in the scheme you describe.
                    >

                    I don't think so because there is effectively a maximum bid. If a regular nurse bids too high the hospital will use a temp agency nurse at a fixed price. However, they would rather use their own nurses.
                  • warren_d_smith31
                    What you said doesn t really make sense. You said nurses assign utility to each shift&wage combination, and we maximize summed utility subject to constraints.
                    Message 9 of 21 , Sep 2, 2009
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                      What you said doesn't really make sense.
                      You said nurses assign utility to each shift&wage combination, and we maximize summed utility subject to constraints. But there are an infinite number of shift&wage combinations since unboundedly high wages are thinkable, and presumably nurses assign higher
                      utility to higher wages, so the optimum is to pay them all an infinite amount of money. This would be prevented by the constraints I assume, in which case optimum is to pay them all available money. Well, ok, that's fine I guess, except the hospital's notion of "optimal" is undoubtably rather different... and more like the opposite.

                      Anyway, what you have described (actually I'm still not sure what it is you want exactly, but it doesn't matter because I understand enough to say the following) IS
                      efficiently soluble to find the exact optimum.

                      What I mean by "efficient" is (what computer scientists generally mean) "low order polynomial time."

                      Why? Because what we have here is a problem called a "bipartite matching" also viewable
                      as a "max flow" problem in directed graphs. E.g. it is well known (although the algorithms are not trivial) that you can find the max-summed-score bipartite matching in
                      an NxM matrix, in polynomial(N,M) time. All these things also are expressible as "linear programs" (although again, proving that works, is not trivial). The point is all your
                      constraints are linear constraints, and the utility-sum thing you optimize is a linear
                      function... hence the whole ball of wax is a linear program. The nontrivial part is that the optimum actually corresponds to a valid matching of jobs to nurses, and not a "fractional matching" where, say, 1/3 of a nurse is used for one job, etc. I think this theorem is, however, provable. (Definitely it is provable with some classes of constraints; perhaps some kinds would not be permitted, though.)

                      I think for you, the "min-cost max-flow" formulation is the best way to look at it.
                      There are books on these topics, e.g.
                      _Network Flows_ by James B. Orlin, Ravindra K. Ahuja, T. L. Magnanti.
                    • jclawrence2
                      ... The main constraint is that there is a finite budget for nurses. So when you assign shift/wage combinations, the solution has to meet that overall
                      Message 10 of 21 , Sep 4, 2009
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                        --- In RangeVoting@yahoogroups.com, "warren_d_smith31" <wds@...> wrote:
                        >
                        > What you said doesn't really make sense.
                        > You said nurses assign utility to each shift&wage combination, and we maximize summed utility subject to constraints. But there are an infinite number of shift&wage combinations since unboundedly high wages are thinkable, and presumably nurses assign higher
                        > utility to higher wages, so the optimum is to pay them all an infinite amount of money. This would be prevented by the constraints I assume, in which case optimum is to pay them all available money. Well, ok, that's fine I guess, except the hospital's notion of "optimal" is undoubtably rather different... and more like the opposite.
                        >

                        The main constraint is that there is a finite budget for nurses. So when you assign shift/wage combinations, the solution has to meet that overall budgetary constraint. This presumably would throw out shift/wage utilities for which the wage is too high so most nurses would end up with a shift/wage that represents less than their highest utilty. However, since we are trying to maximize utility, the final assignment of shifts/wages would tend to use up the available budget.
                      • warren_d_smith31
                        ... --consider this maximum weighted bipartite matching problem. Make this bipartite graph. It has 1 red vertex for each nurse, 1 blue vertex for each
                        Message 11 of 21 , Sep 4, 2009
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                          --- In RangeVoting@yahoogroups.com, "jclawrence2" <j.c.lawrence@...> wrote:
                          >
                          > --- In RangeVoting@yahoogroups.com, "warren_d_smith31" <wds@> wrote:
                          > >
                          > > What you said doesn't really make sense.
                          > > You said nurses assign utility to each shift&wage combination, and we maximize summed utility subject to constraints. But there are an infinite number of shift&wage combinations since unboundedly high wages are thinkable, and presumably nurses assign higher
                          > > utility to higher wages, so the optimum is to pay them all an infinite amount of money. This would be prevented by the constraints I assume, in which case optimum is to pay them all available money. Well, ok, that's fine I guess, except the hospital's notion of "optimal" is undoubtably rather different... and more like the opposite.
                          > >
                          >
                          > The main constraint is that there is a finite budget for nurses. So when you assign shift/wage combinations, the solution has to meet that overall budgetary constraint. This presumably would throw out shift/wage utilities for which the wage is too high so most nurses would end up with a shift/wage that represents less than their highest utility. However, since we are trying to maximize utility, the final assignment of shifts/wages would tend to use up the available budget.


                          --consider this "maximum weighted bipartite matching" problem.
                          Make this bipartite graph. It has 1 red vertex for each nurse,
                          1 blue vertex for each shift-job.
                          The arcs go from each nurse to all shifts (red-->blue arcs)
                          and are labeled with their utilities U and costs C with C>0.
                          There can be multiple arcs between a nurse and a shift, like
                          this
                          Nurse====Shift
                          exhibiting 2 arcs (2 different bids by same nurse).

                          The mission is to find a "matching" in the graph, that is, a subset of
                          its edges such that each blue vertex has exactly one matching-edge
                          emanating from it. And let us, among all matchings, select the one
                          which maximizes the sum (over all its edges ab) of
                          F = U(ab) + lambda*C(ab).
                          Here lambda is some fixed signed real number (a "lagrange multiplier"). Note for any fixed lambda all multiple arcs from a to b
                          can be removed except for just e of them (the one with maximum F).

                          There are pretty simple and efficient algorithms to find the maximum weight matching in a bipartite graph, given any particular input value of lambda. (This also is called the "assignment problem" in the literature.) E.g. the "Hungarian algorithm."
                          http://csclab.murraystate.edu/bob.pilgrim/445/munkres.html
                          http://www.public.iastate.edu/~ddoty/HungarianAlgorithm.html

                          So pick some lambda and find the MWM. The resulting matching will have some total utility we call U(lambda) and some total cost we call C(lambda), and some total F call it F(lambda)=U+lambda*C. One can argue from multiD geometrical picture that F(lambda) is a
                          piecewise-linear continuous function.
                          Furthermore, C(lambda) ought to be monotonic stairstep-type function.

                          Now do an outer binary search on lambda to find the unique magic lambda which causes C(lambda)=Budget. Actually, in general you will not be able to get exact equality but will find a lambda such
                          that if lambda were infinitesimally decreased you'd be below budget and if infinitesimally increased you'd be over budget.

                          Infinitesimally below this magic lambda,
                          I presume(?) that the matching found will be one which maximizes total utility under the constraint that the cost-sum maximally-eats (but not overeats) the budget.

                          [And I think my "presumption" can be proven if we consider a "smoothed version" of the multiD assignment polytope, e.g. all points within distance epsilon of it, then take the limit epsilon-->0+.]

                          The "assignment problem" was actually originally invented
                          to solve a problem quite similar to the nurses+shifts problem,
                          except that was all about costs and not involving utilities.
                          Namely the hospital (or manufacturer, or whatever you call it) was
                          just trying to minimize its expenses, period.

                          This version now adds utilities to the mix, and can do it by adding
                          a lagrange multiplier to the picture. Unfortunately I think
                          this version would be less popular with manufacturers and hospitals... albeit more popular with employees...
                          My outer binary search causes a log-factor slowdown which could probably be avoided by a more sophisticated algorithm.
                          There is a literature called "parametric linear programming" about that issue.

                          --Warren D. Smith 4 Sept 2009
                        • warren_d_smith31
                          Unfortunately, my optimum-utility solution for Shift Bidding problem will fail in real life. It seems to me it works if all the nurses are honest about their
                          Message 12 of 21 , Sep 4, 2009
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                            Unfortunately, my optimum-utility solution for "Shift Bidding" problem will fail in real life.

                            It seems to me it works if all the nurses are honest about their utilities. However, suppose some nurse falsely claims that
                            if a goodly fraction of the entire budget were awarded just to her for her one shift, she'd get infinite utility.
                            Meanwhile all the other nurses bid honestly.

                            Oops.

                            In view of that, pretty soon the nurses would catch on and they'd all provide ludicrous dishonest utility info in their bids. It'd totally break.
                          • Raph Frank
                            ... You could start with a default configuration and then allow negotiation away from that position. For example, each nurse could be given an equal share of
                            Message 13 of 21 , Sep 4, 2009
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                              On Fri, Sep 4, 2009 at 1:04 PM, jclawrence2<j.c.lawrence@...> wrote:
                              > However, since we are trying
                              > to maximize utility, the final assignment of shifts/wages would tend to use
                              > up the available budget.

                              You could start with a "default" configuration and then allow
                              negotiation away from that position.

                              For example, each nurse could be given an equal share of night and day
                              shifts (say 1 week night, 1 week morning and 1 week evening).

                              The nurse can then participate in the bidding process and if they get
                              a bad deal can revert back to the standard. Likewise, the hospital
                              could decide to assign a nurse to her standard shift if the only way
                              to fill all the slots ends up costing more than standard.

                              The effect should be that both sides "win". The nurses get better
                              shifts and the hospital pays less money.
                            • Raph Frank
                              ... I posted on the other thread, an option. A slight variant would be to have an automatic shift trading system. You enter your utility for each shift and
                              Message 14 of 21 , Sep 4, 2009
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                                On Fri, Sep 4, 2009 at 5:29 PM, warren_d_smith31<wds@...> wrote:
                                > In view of that, pretty soon the nurses would catch on and they'd all
                                > provide ludicrous dishonest utility info in their bids. It'd totally break.

                                I posted on the other thread, an option.

                                A slight variant would be to have an automatic shift trading system.

                                You enter your utility for each shift and then the system negotiates
                                on your behalf to try to get you shifts you want.

                                The trade could include a payment. For example, "I want to work days,
                                so if you swap with me I will pay you $1 per hour". The effect is
                                that the person who has made the offer ends up working for $1 per hour
                                less and the other person ends up working for $1 per hour more for
                                that shift.

                                This would mean that the nurses get 100% of the consumer surplus from
                                the operation of the system and the hospital gets nothing. It would
                                probably decrease union opposition to the plan.
                              • jclawrence2
                                ... You can t presime that nurses will assign higher utility to higher wages. Some nurses may assign zero utility to night shifts at any wage because they are
                                Message 15 of 21 , Sep 4, 2009
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                                  --- In RangeVoting@yahoogroups.com, "jclawrence2" <j.c.lawrence@...> wrote:
                                  >
                                  > --- In RangeVoting@yahoogroups.com, "warren_d_smith31" <wds@> wrote:

                                  > > You said nurses assign utility to each shift&wage combination, and we maximize summed utility subject to constraints. But there are an infinite number of shift&wage combinations since unboundedly high wages are thinkable, and presumably nurses assign higher
                                  > > utility to higher wages, so the optimum is to pay them all an infinite amount of money.

                                  You can't presime that nurses will assign higher utility to higher wages. Some nurses may assign zero utility to night shifts at any wage because they are single mothers that need to be home at nioght with their children. They are not simply assigning utility to a wage but to a wage/shift combination.
                                • jclawrence2
                                  ... The nurse can assign zero utility to any shift she really doesn t want. Any shift/wage combination that she assigns a positive utility to would be one that
                                  Message 16 of 21 , Sep 4, 2009
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                                    --- In RangeVoting@yahoogroups.com, Raph Frank <raphfrk@...> wrote:

                                    > The nurse can then participate in the bidding process and if they get
                                    > a bad deal can revert back to the standard. Likewise, the hospital
                                    > could decide to assign a nurse to her standard shift if the only way
                                    > to fill all the slots ends up costing more than standard.
                                    >
                                    > The effect should be that both sides "win". The nurses get better
                                    > shifts and the hospital pays less money.
                                    >

                                    The nurse can assign zero utility to any shift she really doesn't want. Any shift/wage combination that she assigns a positive utility to would be one that she would be willing to work. This should fill most of the slots, but there is always recourse to the temp agency for unfilled shifts. The hospital should end up paying the same amount of money because the idea is to maximize nurses' utility within the overall budget constraint which has been set perhaps by a negotiation between hospital management and the nurses' union. The average shift wage would be the overall budget divided by the number of nurses. Some nurses might make more and some less than average over any given time period. Utility is assigned to a shift/wage combo and not just to a shift.
                                  • jclawrence2
                                    ... I assume that all utilities are between 0 and 1. Furthermore, by the mean based thresholding theorem that you proved, the optimum strategy for each nurse
                                    Message 17 of 21 , Sep 4, 2009
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                                      --- In RangeVoting@yahoogroups.com, "warren_d_smith31" <wds@...> wrote:
                                      >
                                      > Unfortunately, my optimum-utility solution for "Shift Bidding" problem will fail in real life.
                                      >
                                      > It seems to me it works if all the nurses are honest about their utilities. However, suppose some nurse falsely claims that
                                      > if a goodly fraction of the entire budget were awarded just to her for her one shift, she'd get infinite utility.
                                      > Meanwhile all the other nurses bid honestly.
                                      >
                                      > Oops.
                                      >
                                      > In view of that, pretty soon the nurses would catch on and they'd all provide ludicrous dishonest utility info in their bids. It'd totally break.
                                      >

                                      I assume that all utilities are between 0 and 1. Furthermore, by the mean based thresholding theorem that you proved, the optimum strategy for each nurse would be to use approval voting after she assigned her utilities hence the range-approval hybrid. Wouldn't this assure that the system couldn't be gamed?
                                    • Raph Frank
                                      ... There is nothing special about zero utility. Presumably, by zero utility you mean that the nurse is indifferent between taking the shift and not working?
                                      Message 18 of 21 , Sep 5, 2009
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                                        On Sat, Sep 5, 2009 at 4:26 AM, jclawrence2<j.c.lawrence@...> wrote:
                                        >
                                        > The nurse can assign zero utility to any shift she really doesn't want. Any
                                        > shift/wage combination that she assigns a positive utility to would be one
                                        > that she would be willing to work. This should fill most of the slots, but
                                        > there is always recourse to the temp agency for unfilled shifts.

                                        There is nothing special about zero utility. Presumably, by zero
                                        utility you mean that the nurse is indifferent between taking the
                                        shift and not working?

                                        In that case, it is worth paying the nurse to work. There would be a
                                        need to rate the shifts from -1 to +1.

                                        This would allow the hospital to assign the nurse a +1 and a -0.1
                                        shift, instead of having someone from the temp agency handle it. If
                                        the nurse won't work the -0.1 shift, then they might be assigned a
                                        +0.5 shift, so is worse off.

                                        > The
                                        > hospital should end up paying the same amount of money because the idea is
                                        > to maximize nurses' utility within the overall budget constraint which has
                                        > been set perhaps by a negotiation between hospital management and the
                                        > nurses' union.

                                        Well, any pay to the temp agency would probably be considered
                                        "leaking" of money from the nurses.

                                        Also, by prohibiting the hospital from benefiting from the system, you
                                        are decreasing the chances of the hospital setting up the system.

                                        > The average shift wage would be the overall budget divided by
                                        > the number of nurses. Some nurses might make more and some less than average
                                        > over any given time period. Utility is assigned to a shift/wage combo and
                                        > not just to a shift.

                                        I think you are making it to complex for the nurses. In most cases,
                                        the benefit for the nurses of more pay would be a linear increase in
                                        utility.

                                        The nurse could just rate all the shifts in terms of dollars.
                                      • jclawrence2
                                        ... No! There are some shifts that a nurse just might not want to work. For instance,a family member is getting married on a certain date. She would not want
                                        Message 19 of 21 , Sep 5, 2009
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                                          --- In RangeVoting@yahoogroups.com, Raph Frank <raphfrk@...> wrote:
                                          >
                                          > On Sat, Sep 5, 2009 at 4:26 AM, jclawrence2<j.c.lawrence@...> wrote:
                                          > >
                                          > > The nurse can assign zero utility to any shift she really doesn't want. Any
                                          > > shift/wage combination that she assigns a positive utility to would be one
                                          > > that she would be willing to work. This should fill most of the slots, but
                                          > > there is always recourse to the temp agency for unfilled shifts.
                                          >
                                          > There is nothing special about zero utility. Presumably, by zero
                                          > utility you mean that the nurse is indifferent between taking the
                                          > shift and not working?

                                          No! There are some shifts that a nurse just might not want to work. For instance,a family member is getting married on a certain date. She would not want to work any shifts that date. She shouldn't be FORCED to work. That's the usefulness of assigning zero utility to all shifts on that date.

                                          > > The
                                          > > hospital should end up paying the same amount of money because the idea is
                                          > > to maximize nurses' utility within the overall budget constraint which has
                                          > > been set perhaps by a negotiation between hospital management and the
                                          > > nurses' union.
                                          >
                                          > > The average shift wage would be the overall budget divided by
                                          > > the number of nurses. Some nurses might make more and some less than average
                                          > > over any given time period. Utility is assigned to a shift/wage combo and
                                          > > not just to a shift.
                                          >
                                          > I think you are making it too complex for the nurses. In most cases, the benefit for the nurses of more pay would be a linear increase in
                                          > utility.
                                          >
                                          > The nurse could just rate all the shifts in terms of dollars.

                                          Not at all! Utility is assigned to a shift/wage combination. If it were your father's funeral, you wouldn't want to work any shift that day for any amount of money. Similarly, a single mother might not want to work any night shifts because she would want to be home with her children! Nurses would be able to have a trade-off between working more or working less or working more desirable vs less desirable shifts or having more free time or more money, and those trade-offs could vary over time. Having a variety of choices over one's work/income is what it's about.
                                          >
                                        • Raph Frank
                                          ... Utility is not supposed to be modified if you add a constant to it. There is nothing special about zero utility. The effect you want could be achieved by
                                          Message 20 of 21 , Sep 5, 2009
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                                            On Sat, Sep 5, 2009 at 9:34 PM, jclawrence2<j.c.lawrence@...> wrote:
                                            > No! There are some shifts that a nurse just might not want to work. For
                                            > instance,a family member is getting married on a certain date. She would not
                                            > want to work any shifts that date. She shouldn't be FORCED to work. That's
                                            > the usefulness of assigning zero utility to all shifts on that date.

                                            Utility is not supposed to be modified if you add a constant to it.
                                            There is nothing special about zero utility.

                                            The effect you want could be achieved by the nurse setting the wage at
                                            $100 per hour for that shift.
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