Arnold Kling  

Social Security and Intransitivity

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Riker and the Mathematician's ... Inevitable Tax Increases...

Bryan's post on the doubtful empirical usefulness of social intransitivity is probably right. Nonetheless, suppose that on Social Security there are three political viewpoints--Democratic, Republican, and nonpartisan--and three policy options--status quo, private accounts, and fiscal medicine. By fiscal medicine, I mean tax increases and/or reductions in future promised benefits.

Presumably, Democrats' favorite option is the status quo, and their least favorite is private accounts.

Republicans' favorite option is private accounts, and their least favorite option might be fiscal medicine, because they don't want to be responsible for inflicting pain.

Nonpartisans' favorite option might be fiscal medicine, and their least favorite option might be the status quo.

In that case, we have in terms of rank ordering of options:

DemocratsRepublicansNonpartisans
status quoprivate accountsfiscal medicine
fiscal medicinestatus quoprivate accounts
private accountsfiscal medicinestatus quo

So, two out of three groups favor private accounts over the status quo, two out of three groups favor the status quo over fiscal medicine, and two out of the three groups favor fiscal medicine over private accounts! Intransitivity of social preferences.

In the real world, of course, politicians look for compromises.

For Discussion. Does the usefulness of the concept of a social welfare function stand or fall on its mathematical properties?


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COMMENTS (9 to date)
Boonton writes:

Hmmm, assume the three groups have equal weight and then assign points for their perferences (1 for most desired, 2 for second and 3 for least desired).

...............Rep.......Dem.....Ind......Total
Status Quo.....2.........1.......3........6

Fiscal M.......3........2.........1.......6

Private........1........3.........2.......6

It would appear to be a tie. Each option has at least one group giving it a 1, 2 and a 3. Things get more interesting if we try to assign weights to the various groups as well as account for those who deviate from the sterotype (such as deficit hawk Republicans who would favor fiscal medicine over the status quo). It's a bit of a leap to assume independents would perfer privitization over the status quo. Considering how unpopular Bush's plan appears to be privitization might be the least desirable outcome for both Democrats and Indepens.

Lawrance George Lux writes:

I agree with Boonton, and also would issue one caveat: Social programs are like Politicians themselves, standing a far better chance of getting re-elected over an unkown Candidate. lgl

Duane Gran writes:

The chart leaves off the position of those who would prefer to see social welfare expanded, which isn't a view monopolized by Democrats. The current environment has progressives on the defensive, such that status quo is the new left position for most.

spencer writes:

It does not stand on its mathmatical properties because it excludes too many posibilities.

It does not include this possibility.

I am a democrat that thinks private accounts are a good idea. But it is a shame because of the Bush deficits we can not afford the transition costs -- or whatever you want to label them --
to shift to private accounts.

Deb McAdams writes:

This is somewhat OT to the main point being made, but the idea that private accounts are an alternative to benefit cuts and/or tax increases is somewhere between not true and deliberately misleading in the context of the present debate.

Certainly there has not been a proposal made by anyone to institute private accounts without rather extreme "fiscal medicine" on current expected beneficiaries.

Bret Perkins writes:

As spencer points out, it is possible for intransitivity to exist within groups, if two individuals who both claim to be Dems have differing opinions on the valuation of SS choices. However, this shouldnt be a concern. What is more relevant is the transitivity of choice within the groups as a whole; ie: the majority of Dems prefer their SS choice valuation to that of Reps and Indeps., and the same holds that Reps prefer theirs to the other two, and Indeps prefer theirs to the other two.
Why be concerned with intransitivity among the three groups as a whole? It seems to be an arbitrary assignment for looking at transitivity. What is important is that Dems, Reps, and Indeps maintain transitivity of choice within their respective groups.

Deb McAdams writes:

But if privatization without "fiscal medicine" was possible, democrats would much prefer that to fiscal medicine.

Which pretty thoroughly overturns the entire model and defeats its point.

Once misdirections are put aside, this is really a debate between as little fiscal medicine as possible to sustain the program, or enough fiscal medicine to dismantle the program.

A simple one-dimensional set of decisions that can be looked at using any standard analysis of politics.

Edge writes:

If it were so simple.

But this hasn't defined a problem to be solved. Private accounts, by themselves create a bigger fiscal problem than was there in the first place, at least for anyone already in the workplace. So while independents might place the "status quo" lowest in an opinion survey, and the might be neutral on private accounts, the preference for fiscal solvency might trump the neutrality on private accounts.

As a matter of political calculus, that might be solved with propaganda. But so far, at least, propaganda has seemed to work against that hypothesis.

There's also the question; would Republicans tolerate any solution that leads to fiscal solvency, or any framing of the question in which solvency is the problem to be solved?

Tom writes:

Does the usefulness of the concept of a social welfare function stand or fall on its mathematical properties?

The concept of a "social welfare function" (with or without mathematical properties) is meaningless. You can write equations until kingdom come, but no equation you write can make commensurate the happiness or unhappiness of individuals.

Consider the case in which a nation (call it US) is formed in order to defend its citizens from outside attack by an enemy nation (call it AQ). (That's the main reason the United States was formed, strange as it may now seem.) Assuming that the citizens of US are unanimous in their opposition to AQ, and unanimous in their support of measures taken to deter AQ, each of them will be happier if their unified support actually deters an attack by AQ. But AQ will be unhappy (or less happy) because it can't attack US with impunity. The happiness of US (even if it could be expressed mathematically), isn't offset by the unhappiness of AQ (even if it could be expressed mathematically). In fact, US's happiness is increased by AQ's unhappiness, even though neither can be quantified.

Suppose, however, that a faction of US citizens (call it LW) is unhappy because of certain actions being taken to prevent an attack by AQ. The actions that make LW unhappy don't make me unhappy. In fact, they add to my happiness because I despise LW; anything that makes LW unhappy makes me happier. Thus, I'll continue to be happy, despite LW's unhappiness, unless and until (a) LW's unhappiness leads to a political decision to stop defending US against AQ or (b) AQ attacks US successfully.

I could go on, but I think you get the idea. My happiness (or unhappiness) is mine, and yours is yours. The best we can say is that voluntary exchange in free markets, protected by strict enforcement of laws against force and fraud, would make almost everyone happier -- and wealthier. So much wealthier that there'd be plenty of money with which to buy off the free-loaders. But that's another story.

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