The chilling effect of that risk, it is feared, will discourage regulation in the public interest and in effect put a ratchet under the neoliberal agenda of the 1980s.
It tends to be assumed that governments are the good guys and corporations the bad guys in such disputes. The latter are rarely seen, for example, as the custodians of people's retirement savings.
A lot of the suspicion directed at the ISDS provisions, and of the TPP in general, is fear of the unknown. We can't be sure what the agreement will say.
ISDS provisions are commonplace in international investment agreements, which now number more than 3000 worldwide, but that does not mean they are frequently invoked.
The United Nations Conference on Trade and Development (UNCTAD) monitors them. In a report last month it noted a trend in 13 intentional investment agreements concluded last year to limit their scope and circumscribe the right of recourse to arbitration.
Eleven have general exceptions - for example, the protection of human, animal or plant life or health, or the conservation of exhaustible natural resources.
"These sustainable development features are supplemented by treaty elements that aim more broadly at preserving regulatory space for public policies of host countries and/or at minimising exposure to investment arbitration." Whether the TPP conforms to this trend remains to be seen, but in the meantime it is instructive to look at UNCTAD data on ISDS cases taken last year.
Of the 42 cases decided last year, only 33 are in the public domain. Transparency is clearly one of the issues about this process.
There were 42 - down from 59 in 2013 and in line with the average from 2003 to 2011. By the end of 2014 the number of concluded cases before the investor-state tribunals - most of them in the past decade - was 356.
"Out of these, approximately 37 per cent (132 cases) were decided in favour of the state (all claims dismissed either on jurisdictional grounds or on the merits), and 25 per cent (87 cases) ended in favour of the investor (monetary compensation awarded). Approximately 28 per cent of cases (101) were settled and 8 per cent of claims (29) were discontinued for reasons other than settlement," UNCTAD said.
Of the 42 cases decided last year, only 33 are in the public domain. Transparency is clearly one of the issues about this process.
Of those, 15 were decisions on merits - the rest were mainly about the jurisdiction of the tribunals, for which the results split 50:50 - and the tribunals found for the investors in 10 cases and for the state in the other five.
The compensation awarded included US$50 billion ($68 billion) in three related cases. They were taken by shareholders in the former Russian oil company Yukos, against the Russian Federation.
That might prove difficult to enforce.
Before that the largest compensation award was US$1.8 billion (plus interest) to Occidental Petroleum against Ecuador in 2012.
Of the cases filed last year, half related to electricity generation (including the weakening of subsidies for renewables), oil and gas, and mining.
US Senator Elizabeth Warren, a leading Democrat, recently criticised ISDS provisions in the TPP.
Representatives of some key European countries have said they would not support including an ISDS in the Transatlantic Trade and Investment Partnership, which the European Union and the United States are negotiating, UNCTAD said.
Essentially, their argument is that foreign investors, like domestic ones, should be able to rely on the courts of the countries in which they invest. If they cannot, then caveat investor.
Responding to Warren, the White House, in the person of Jeff Zients, director of the National Economic Council, assures us the TPP "will make it absolutely clear that governments can regulate in the public interest, including with regard to health, safety and the environment, and narrow the definition of what kinds of injuries investors can seek compensation for." All arbitration proceedings under TPP would be open, he said, and non-parties, including labour unions and civil society organisations, would be able to file briefs to inform the outcome of cases.
Suing is one thing, winning is another. And as the saying goes "hard cases make bad law".
Warren, like other critics of ISDS, argues it is hard to have confidence in tribunals made up of "highly paid corporate lawyers [who] go back and forth between representing corporations one day and sitting in judgment the next".
The White House response was that the arbitration rules used under TPP would "require the independence of arbitrators and provide for challenge and disqualification in the event of conflict of interest or bias. They also provide a central role for the government being sued to determine which arbitrators hear the case." That is unlikely to satisfy those who are dubious of a system in which arbitrators can be litigators one day and judges the next, and whose decisions cannot be appealed.
Inevitably, among the hundreds of cases which have been taken to these tribunals are some which are bound to make lips curl, like big tobacco companies suing small poor countries (or even Australia), or a US oil company seeking redress against Canadian provincial regulation unfriendly to fracking.
But suing is one thing, winning is another. And as the saying goes "hard cases make bad law".
Investor-state dispute settlement
What is it?
Mechanism that allows an investor to go to an arbitration tribunal, to settle a dispute with a foreign government. Included in many trade deals
Is it used often?
356 cases concluded so far
Who wins?
The state 37%
The investor 25%
Settled 28%
Discontinued 8%
- Figures: UN Conference on Trade and Development
See the Unctad report here.